Package 'DataVisualizations'

Title: Visualizations of High-Dimensional Data
Description: Gives access to data visualisation methods that are relevant from the data scientist's point of view. The flagship idea of 'DataVisualizations' is the mirrored density plot (MD-plot) for either classified or non-classified multivariate data published in Thrun, M.C. et al.: "Analyzing the Fine Structure of Distributions" (2020), PLoS ONE, <DOI:10.1371/journal.pone.0238835>. The MD-plot outperforms the box-and-whisker diagram (box plot), violin plot and bean plot and geom_violin plot of ggplot2. Furthermore, a collection of various visualization methods for univariate data is provided. In the case of exploratory data analysis, 'DataVisualizations' makes it possible to inspect the distribution of each feature of a dataset visually through a combination of four methods. One of these methods is the Pareto density estimation (PDE) of the probability density function (pdf). Additionally, visualizations of the distribution of distances using PDE, the scatter-density plot using PDE for two variables as well as the Shepard density plot and the Bland-Altman plot are presented here. Pertaining to classified high-dimensional data, a number of visualizations are described, such as f.ex. the heat map and silhouette plot. A political map of the world or Germany can be visualized with the additional information defined by a classification of countries or regions. By extending the political map further, an uncomplicated function for a Choropleth map can be used which is useful for measurements across a geographic area. For categorical features, the Pie charts, slope charts and fan plots, improved by the ABC analysis, become usable. More detailed explanations are found in the book by Thrun, M.C.: "Projection-Based Clustering through Self-Organization and Swarm Intelligence" (2018) <DOI:10.1007/978-3-658-20540-9>.
Authors: Michael Thrun [aut, cre, cph] , Felix Pape [aut, rev], Onno Hansen-Goos [ctr, ctb], Quirin Stier [ctb, rev] , Hamza Tayyab [ctr, ctb], Luca Brinkmann [ctr, ctb], Dirk Eddelbuettel [ctr], Craig Varrichio [ctr], Alfred Ultsch [dtc, ctb, ctr]
Maintainer: Michael Thrun <[email protected]>
License: GPL-3
Version: 1.3.3
Built: 2024-10-29 10:22:19 UTC
Source: https://github.com/mthrun/datavisualizations

Help Index


Visualizations of High-Dimensional Data

Description

Gives access to data visualisation methods that are relevant from the data scientist's point of view. The flagship idea of 'DataVisualizations' is the mirrored density plot (MD-plot) for either classified or non-classified multivariate data published in Thrun, M.C. et al.: "Analyzing the Fine Structure of Distributions" (2020), PLoS ONE, <DOI:10.1371/journal.pone.0238835>. The MD-plot outperforms the box-and-whisker diagram (box plot), violin plot and bean plot and geom_violin plot of ggplot2. Furthermore, a collection of various visualization methods for univariate data is provided. In the case of exploratory data analysis, 'DataVisualizations' makes it possible to inspect the distribution of each feature of a dataset visually through a combination of four methods. One of these methods is the Pareto density estimation (PDE) of the probability density function (pdf). Additionally, visualizations of the distribution of distances using PDE, the scatter-density plot using PDE for two variables as well as the Shepard density plot and the Bland-Altman plot are presented here. Pertaining to classified high-dimensional data, a number of visualizations are described, such as f.ex. the heat map and silhouette plot. A political map of the world or Germany can be visualized with the additional information defined by a classification of countries or regions. By extending the political map further, an uncomplicated function for a Choropleth map can be used which is useful for measurements across a geographic area. For categorical features, the Pie charts, slope charts and fan plots, improved by the ABC analysis, become usable. More detailed explanations are found in the book by Thrun, M.C.: "Projection-Based Clustering through Self-Organization and Swarm Intelligence" (2018) <DOI:10.1007/978-3-658-20540-9>.

Details

For a brief introduction to DataVisualizations please see the vignette A Quick Tour in Data Visualizations.

Please see https://www.deepbionics.org/. Depending on the context please cite either [Thrun, 2018] regarding visualizations in the context of clustering or [Thrun/Ultsch, 2018] for other visualizations.

For the Mirrored Density Plot (MD plot) please cite [Thrun et al., 2020] and see the extensive vignette in https://md-plot.readthedocs.io/en/latest/index.html. The MD plot is also available in Python https://pypi.org/project/md-plot/

Index of help topics:

ABCbarplot              Barplot with Sorted Data Colored by ABCanalysis
AccountingInformation_PrimeStandard_Q3_2019
                        Accounting Information in the Prime Standard in
                        Q3 in 2019 (AI_PS_Q3_2019)
BimodalityAmplitude     Bimodality Amplitude
CCDFplot                plot Complementary Cumulative Distribution
                        Function (CCDF) in Log/Log uses ecdf, CCDF(x) =
                        1-cdf(x)
ChoroplethPostalCodesAndAGS_Germany
                        Postal Codes and AGS of Germany for a
                        Choropleth Map
Choroplethmap           Plots the Choropleth Map
ClassBarPlot            ClassBarPlot
ClassBoxplot            Creates Boxplot plot for all classes
ClassErrorbar           ClassErrorbar
ClassMDplot             Class MDplot for Data w.r.t. all classes
ClassPDEplot            PDE Plot for all classes
ClassPDEplotMaxLikeli   Create PDE plot for all classes with maximum
                        likelihood
Classplot               Classplot
CombineCols             Combine vectors of various lengths
CombineRows             Combine matrices of various lengths
Crosstable              Crosstable plot
DataVisualizations-package
                        Visualizations of High-Dimensional Data
DefaultColorSequence    Default color sequence for plots
DensityContour          Contour plot of densities
DensityScatter          Scatter plot with densities
DiagnosticAbility4Classifiers
                        DiagnosticAbility4Classifiers
DrawWorldWithCls        Plot a classificated world map
DualaxisClassplot       Dualaxis Classplot
DualaxisLinechart       DualaxisLinechart
Fanplot                 The fan plot
FundamentalData_Q1_2018
                        Fundamental Data of the 1st Quarter in 2018
GermanPostalCodesShapes
                        GermanPostalCodesShapes
GoogleMapsCoordinates   Google Maps with marked coordinates
Heatmap                 Heatmap for Clustering
HeatmapColors           Default color sequence for plots
ITS                     Income Tax Share
InspectBoxplots         Inspect Boxplots
InspectCorrelation      Inspect the Correlation
InspectDistances        Inspection of Distance-Distribution
InspectScatterplots     Pairwise scatterplots and optimal histograms
InspectStandardization
                        QQplot of Data versus Normalized Data
InspectVariable         Visualization of Distribution of one variable
JitterUniqueValues      Jitters Unique Values
Lsun3D                  Lsun3D inspired by FCPS [Thrun/Ultsch, 2020]
                        introduced in [Thrun, 2018]
MAplot                  Minus versus Add plot
MDplot                  Mirrored Density plot (MD-plot)
MDplot4multiplevectors
                        Mirrored Density plot (MD-plot)for Multiple
                        Vectors
MTY                     Muncipal Income Tax Yield
Meanrobust              Robust Empirical Mean Estimation
Multiplot               Plot multiple ggplots objects in one panel
OpposingViolinBiclassPlot
                        OpposingViolinBiclassPlot
OptimalNoBins           Optimal Number Of Bins
PDEnormrobust           PDEnormrobust
PDEplot                 PDE plot
ParetoDensityEstimation
                        Pareto Density Estimation V3
ParetoRadius            ParetoRadius for distributions
Piechart                The pie chart
Pixelmatrix             Plot of a Pixel Matrix
Plot3D                  3D plot of points
PlotGraph2D             PlotGraph2D
PlotMissingvalues       Plot of the Amount Of Missing Values
PlotProductratio        Product-Ratio Plot
PmatrixColormap         P-Matrix colors
QQplot                  QQplot with a Linear Fit
ROC                     ROC plot
RobustNorm_BackTrafo    Transforms the Robust Normalization back
RobustNormalization     RobustNormalization
ShepardDensityScatter   Shepard PDE scatter
Sheparddiagram          Draws a Shepard Diagram
SignedLog               Signed Log
Silhouetteplot          Silhouette plot of classified data.
Slopechart              Slope Chart
StatPDEdensity          Pareto Density Estimation
Stdrobust               Standard Deviation Robust
Worldmap                plots a world map by country codes
categoricalVariable     A categorical Feature.
estimateDensity2D       estimateDensity2D
stat_pde_density        Calculate Pareto density estimation for ggplot2
                        plots
world_country_polygons
                        world_country_polygons
zplot                   Plotting for 3 dimensional data

Author(s)

Michael Thrun, Felix Pape, Onno Hansen-Goos, Alfred Ultsch

Maintainer: Michael Thrun <[email protected]>

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Thrun et al., 2020] Thrun, M. C., Gehlert, T. & Ultsch, A.: Analyzing the Fine Structure of Distributions, PLoS ONE, Vol. 15(10), pp. 1-66, DOI 10.1371/journal.pone.0238835, 2020.

Examples

data("Lsun3D")
Data=Lsun3D$Data

Pixelmatrix(Data)



InspectDistances(as.matrix(dist(Data)))


MAlist=MAplot(ITS,MTY)

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data
#clear cluster structure
plot(Data[,1:2],col=Cls)
#However, the silhouette plot does not indicate a very good clustering in cluster 1 and 2

Silhouetteplot(Data,Cls = Cls)


Heatmap(as.matrix(dist(Data)),Cls = Cls)

Barplot with Sorted Data Colored by ABCanalysis

Description

This plot can be read like a scree plot for PCA. It allowed to select the most important values visually.

Usage

ABCbarplot(Data,

Colors=DataVisualizations::DefaultColorSequence[1:3],

main,xlab,ylab="Value")

Arguments

Data

[1:n] vector of Data, e.g. eigenvalues of PCA

Colors

three colors for A, B and C

main

title of plot

xlab

xlabel

ylab

ylabel

Details

ABC analysis is explained in ABCanalysis. The visualization is based on ggplot2.

Value

List V of

ABCanalysis

output of ABCanalysis

ggobject

object of ggplot2 plotted

DF

Data frame if another plot should be done manually

Author(s)

Michael Thrun

References

Ultsch. A ., Lotsch J.: Computed ABC Analysis for Rational Selection of Most Informative Variables in Multivariate Data, PloS one, Vol. 10(6), pp. e0129767. doi 10.1371/journal.pone.0129767, 2015.

See Also

ABCanalysis

Examples

data('FundamentalData_Q1_2018')
Data=as.matrix(FundamentalData_Q1_2018$Data)
Data[!is.finite(Data)]=0
results=prcomp(Data)
main="Scree plot with Class A of the Most-Important Eigenvalues"
plotlist = ABCbarplot(results$sdev,ylab='Eigenvalues',main=main)
plotlist$ggobject

Accounting Information in the Prime Standard in Q3 in 2019 (AI_PS_Q3_2019)

Description

Accounting Information of 261 companies traded in the Frankfurt stock exchange in the German Prime standard.

Usage

data("AccountingInformation_PrimeStandard_Q3_2019")

Format

A list with of three objects

Key

[1:n] Key of the 261 obeservations

Data

[1:n,1:d] numeric matrix of 261 observations on the 45 variables describing the accounting information

Cls

[1:n] a numeric vector of k clusters of the clustering performend in [Thrun/Ultsch, 2019]

Details

Detailed data description can be found in [Thrun/Ultsch, 2019].

Source

Yahoo Finance

References

[Thrun/Ultsch, 2019] Thrun, M. C., & Ultsch, A.: Stock Selection via Knowledge Discovery using Swarm Intelligence with Emergence, IEEE Intelligent Systems, Vol. under review, pp., 2019.

Examples

data(AccountingInformation_PrimeStandard_Q3_2019)

str(AI_PS_Q3_2019)
dim(AI_PS_Q3_2019$Data)

Bimodality Amplitude

Description

Computes the Bimodality Amplitude of [Zhang et al., 2003]

Usage

BimodalityAmplitude(x, PlotIt=FALSE)

Arguments

x

Data vector.

PlotIt

FALSE, TRUE if a figure with the antimodes and peaks is plotted

Details

This function calculates the Bimodality Ampltiude of a data vector. This is a measure of the proportion of bimodality and the existence of bimodality. The value lies between zero and one (that is: [0,1]) where the value of zero implies that the data is unimodal and the value of one implies the data is two point masses.

Note

function was rewritten after the flow of a function of Sathish Deevi because the original function was incorrect.

Author(s)

Michael Thrun

References

Zhang, C., Mapes, B., & Soden, B.: Bimodality in tropical water vapour, Quarterly Journal of the Royal Meteorological Society, Vol. 129(594), pp. 2847-2866, 2003.

Examples

#Example 1
data<-c(rnorm(299,0,1),rnorm(299,5,1))
BimodalityAmplitude(data,TRUE)

#Example 2
dist1<-rnorm(2100,5,2)
dist2<-dist1+11
data<-c(dist1,dist2)

BimodalityAmplitude(data,TRUE)

#Example 3
dist1<-rnorm(210,-15,1)
dist2<-rep(dist1,3)+30
data<-c(dist1,dist2)

BimodalityAmplitude(data,TRUE)

#Example 4
data<-runif(1000,-15,1)

BimodalityAmplitude(data,TRUE)

A categorical Feature.

Description

Character vector of length 391029 with five different labels.

Usage

data("categoricalVariable")

Examples

data(categoricalVariable)
unique(categoricalVariable)

plot Complementary Cumulative Distribution Function (CCDF) in Log/Log uses ecdf, CCDF(x) = 1-cdf(x)

Description

plot Complementary Cumulative Distribution Function (CCDF) in Log/Log uses ecdf, CCDF(x) = 1-cdf(x)

Arguments

Feature

Vector of data to be plotted, or a matrix with given probability density function in column 2 and/or a cumulative density function in column 3

pch

Optional, default: pch=0 for Line, other numbers see documentation about pch of plot

PlotIt

Optional, if PlotIt==T (default) do a plot, otherwise return only values

LogLogPlot

Optional, if LogLogPlot==T (default) do a log/log plot

xlab

Optional, xlab of plot

ylab

Optional, ylab of plot

main

Optional, main of plot

...

Optional, further arguments for plot

Value

V$CCDFuniqX,V$CCDFuniqY CCDFuniqY= 1-cdf(CCDFuniqX), such that plot(CCDFuniqX,CCDFuniqY)...)

Author(s)

Michael Thrun


Plots the Choropleth Map

Description

A thematic map with areas colored in proportion to the measurement of the statistical variable being displayed on the map. A political map geneated by this function was used in the conference talk of the publication [Thrun/Ultsch, 2018].

Usage

Choroplethmap(Counts, PostalCodes, NumberOfBins = 0,

 Breaks4Intervals, percentiles = c(0.5, 0.95), 
 
 digits = 0, PostalCodesShapes, PlotIt = TRUE,

 DiscreteColors, HighColorContinuous = "red",

 LowColorContinuous = "deepskyblue1", NAcolor = "grey",

 ReferenceMap = FALSE, main = "Political Map of Germany",

 legend = "Range of values", Silent = TRUE)

Arguments

Counts

vector [1:m], statistical variable being displayed

PostalCodes

vector[1:n], currently german postal codes (zip codes), if PostalCodesShapes is not changed manually, does not need to be unique

NumberOfBins

Default: 1; 1 or below continously changes the color as defined by the package choroplethr. A Number between 2 and 9 sets equally sized bins. Higher numbers are not allowed

Breaks4Intervals

If NumberOfBins>1 you can set here the intervals of the bins manually

percentiles

If NumberOfBins>1 and Breaks4Intervals not set, then the percentiles of min and max bin can be set here. See also quantile.

digits

number of digits for round

PostalCodesShapes

Specially prepared shape file with postal codes and geographic boundaries. If you set this object, then you can use non german zip codes. You can see the required structure in map.df, github trulia choroplethr blob master r chloropleth. The German PostalCodesShapes can be downloaded from https://github.com/Mthrun/DataVisualizations/tree/master/data.

PlotIt

Either Plot the map directly or change the object manually before plotting it

DiscreteColors

Set the discrete colors manually if NumberOfBins>1, else it is ignored

HighColorContinuous

if NumberOfBins<=1: color of highest continuous value, else it is ignored

LowColorContinuous

if NumberOfBins<=1: color of lowest continuous value, else it is ignored

NAcolor

Color of NA values in the map (postal codes without any counts)

ReferenceMap

TRUE: With Google map, FALSE: without Google map

main

title of plot

legend

title of legend

Silent

TRUE: disable warnings of choroplethr package FALSE: enable warnings of choroplethr package

Details

This wrapper for the choroplethr enables to visualize a political map easily in the case of german zip codes based on given counts and postal codes. Other postal codes are in principle usable.

Value

List of

chorR6obj

An R6 object of the package choroplethr

DataFrame

Transformed PostalCodes and Counts in a way that they can be used in the package choroplethr.

Note

You could read https://www.r-bloggers.com/2016/05/case-study-mapping-german-zip-codes-in-r/, if you want to change the map (PostalCodesShapes shape object).

Author(s)

Michael Thrun

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

See Also

Google choroplethr package.

Examples

#Many postal codes are required to see a structure
#Exemplary two postal codes in the upper left corner of the map
out=Choroplethmap(c(4,8,5,4),

c('49838', '26817', '49838', '26817'),

NumberOfBins=2,PlotIt=FALSE)

out$chorR6obj$render()

#bins are only presented in the map if the have values within
out=Choroplethmap(c(4,8,5,4),c('49838', '26817',

 '49838', '26817'),NumberOfBins=5,
 
 Breaks4Intervals=c(1,2,3,5,10),PlotIt=FALSE)


out$chorR6obj$render()

# Result of [Thrun/Ultsch, 2018]

data('ChoroplethPostalCodesAndAGS_Germany')
res=Choroplethmap(as.numeric(ChoroplethPostalCodesAndAGS_Germany$Cls)+1,

ChoroplethPostalCodesAndAGS_Germany$PLZ,NumberOfBins = 2,

Breaks4Intervals = c(0,1,2,3,4,5,6),digits = 1,ReferenceMap = F,

DiscreteColors = c('white','green','blue','red','magenta'),

main = 'Classification of German Postal Codes based on Income Tax Share and Yield',

legend = 'ITS vs MTY Classification in 2010',NAcolor = 'black',PlotIt=FALSE)


#takes time to process
res$chorR6obj$render()

Postal Codes and AGS of Germany for a Choropleth Map

Description

Zip Codes and Community Identification Number of Germany which can be used in a Choropleth Map.

Usage

data("ChoroplethPostalCodesAndAGS_Germany")

Format

A data frame with 8702 observations on the following 4 variables.

PLZ

German postal codes/zip codes

Cls

Clustering aggregated of germany postal codes by MTY and ITS features

AGS

It is the 'Amtlicher Gemeindeschluessel' (Community Identification Number) of German municipalities

Names

Names of municipalities

Details

CLS are the the labels of a MTS versus ITS Bayesian classification showing two main groups of low quota ('1') and high quota ('2') municipalities. Additionally, outliers are manually classified into two separated groups called sponsors ('3') and promoted ('4'). In the Bayesian Classification non classified data have the label '0'. If a 'AGS' code of a 'PLZ' was unclear than the label is 'NaN'.

Class 0 low quota high quota sponsors promoted non classified unclear mapping
Labels 0 1 2 3 4 5 NaN
CountPerClass 31 1325 7239 10 95 5 2

Source

Generated for [Thrun/Ultsch, 2018] using the approach of [Ultsch/Behnisch, 2017].

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch/Behnisch, 2017] Ultsch, A., Behnisch, M.: Effects of the payout system of income taxes to municipalities in Germany, Applied Geography, Vol. 81, pp. 21-31, 2017.

Examples

data(ChoroplethPostalCodesAndAGS_Germany)
str(ChoroplethPostalCodesAndAGS_Germany)

ClassBarPlot

Description

Represent values for each class and instance as bar plot with optional error deviation, e.g., mean values of features depending on class with standard deviation.

Usage

ClassBarPlot(Values, Cls, Deviation, Names, ylab = "Values",
xlab = "Instances", PlotIt = TRUE)

Arguments

Values

[1:n] Numeric vector with values (y-axis) in matching order to Cls, Deviation and Names.

Cls

[1:n] Numeric vector of classes in matching order to Values and Deviation and Names.

Deviation

[1:n] Numeric vector with deviation in matching order to Values and Cls and Names.

Names

[1:n] Character or numeric vector of instances (x-axis) in matching order to Values and Cls and Deviation.

ylab

Character stating y label.

xlab

Character stating x label.

PlotIt

Logical value indicating visual output TRUE => create visual output FALSE => do not create visual output (Default: Boolean=TRUE).

Value

ggplot2 object

Author(s)

Quirin Stier

Examples

library(ggplot2)

if(require(dplyr)){
  tmpVar1 = iris 
  tmpVar2 = iris 
  tmpVar3 = iris 
  tmpVar4 = iris 
  
  tmpVar5 = iris 
  tmpVar6 = iris 
  tmpVar7 = iris 
  tmpVar8 = iris 
  
  Values    = c(tmpVar1$mean, tmpVar2$mean, tmpVar3$mean, tmpVar4$mean)
  Class     = rep(1:3, 4)
  Deviation = c(tmpVar5$sd, tmpVar6$sd, tmpVar7$sd, tmpVar8$sd)
  
  if(length(Values) == length(Class)){
    ClassBarPlot(Values = Values, Cls = Class, Deviation = Deviation)
  }
  
}

Creates Boxplot plot for all classes

Description

Boxplot the data for all classes

Usage

ClassBoxplot(Data, Cls,  ColorSequence = DataVisualizations::DefaultColorSequence,

 ClassNames = NULL,All=FALSE, PlotLegend = TRUE,

 main = 'Boxplot per Class', xlab = 'Classes', ylab = 'Range of Data')

Arguments

Data

Vector of the data to be plotted

Cls

Vector of class identifiers.

ColorSequence

Optional: The sequence of colors used, Default: DefaultColorSequence()

ClassNames

Optional: The names of the classes. Default: C1 - C(Number of Classes)

All

Optional: adds full data vector for comparison against classes

PlotLegend

Optional: Add a legent to plot. Default: TRUE)

main

Optional: Title of the plot. Default: "ClassBoxPlot""

xlab

Optional: Title of the x axis. Default: "Classes"

ylab

Optional: Title of the y axis. Default: "Data"

Value

A List of

ClassData

The DataFrame used to plot

ggobject

The ggplot2 plot object

in mode invisible

Author(s)

Michael Thrun, Felix Pape

Examples

data(ITS)
#please download package from cran
#model=AdaptGauss::AdaptGauss(ITS)
#Classification=AdaptGauss::ClassifyByDecisionBoundaries(ITS,

#DecisionBoundaries = AdaptGauss::BayesDecisionBoundaries(model$Means,model$SDs,model$Weights))

DataVisualizations::ClassBoxplot(ITS,Classification)$ggobject

ClassErrorbar

Description

Plots ClassErrorbars at Xvalue positions for one or more than one classes with user means and defined whiskers

Usage

ClassErrorbar(Xvalues, Ymatrix, Cls, ClassNames, ClassCols, ClassShape, 

MeanFun = median, SDfun, JitterPosition = 0.5,

main = "Error bar plot", xlab, ylab, WhiskerWidth = 7, Whisker_lwd = 1, BW = TRUE)

Arguments

Xvalues

[1:m] Numerical or character vector, positions of error bars (see details) in on x-axis for the m variables

Ymatrix

[1:n,1:d] of n cases and d=m*k variables with for which the error-bar statistics defined by MeanFun and SDfun should be computed

Cls

Optional, [1:d] numerical vector of k classes for the d variables. Each class is one method that will be shown as distinctive set of error bars in the plot

ClassNames

Optional, [1:k] character vector of k methods

ClassCols

Optional, [1:k] character vector of k colors

ClassShape

Optional, [1:k] numerical vector of k shapes, see pch in Classplot for details

MeanFun

Optional, error bar statstic of mean points, default=median

SDfun

Optional, error bar statstic for the length of whiskers, default is the robust estimation of standard deviation

JitterPosition

Optional, how much in values of Xvalues should the error bars jitter around Xvalues to not overlap

main

Optional, title of plot

xlab

Optional, x-axis label

ylab

Optional, y-axis label

WhiskerWidth

Optional, scalar above zero defining the width of the end of the whiskers

Whisker_lwd

Optional, scalar obove zero defining the thickness of the whisker lines

BW

Optional, FALSE: usual ggplot2 background and style which is good for screen visualizations. Default: TRUE: theme_bw() is used which is more appropriate for publications

Details

If k=1, e.g., one method is used, d=m and Cls=rep(1,m). All vector [1:k] assume the occurance of the classes in Cls as ordered with increasing value.

Statistics are provided in long table format with the column names Xvalues, Mean, SD and Method. The method column specifies the names of the k classes.

If Xvalues is a character vector (see example), ggplot2 automatically sets the position on the x-axis. Otherwise specific numeric positions can be set. This allowes also for plotting a smooth line over the average (see example).

Value

List with

ggobj

The ggplot object of the ClassErrorbar

Statistics

[1:(d*k)1:4] data frame of statstics per class used for plotting

Author(s)

Michael Thrun

Examples

data('FundamentalData_Q1_2018')
Data=as.matrix(FundamentalData_Q1_2018$Data)
Cls = FundamentalData_Q1_2018$Cls
Class1Data = matrix(NA, nrow = nrow(Data), ncol = 2)
Class2Data = matrix(NA, nrow = nrow(Data), ncol = 2)
Class1Data[which(Cls==1), ] = Data[which(Cls==1), c("TotalAssets", "TotalLiabilities")]
Class2Data[which(Cls==2), ] = Data[which(Cls==2), c("TotalAssets", "TotalLiabilities")]
YMatrix = cbind(Class1Data, 
                Class2Data)

#Option 1: character vector
ClassErrorbar(c("TotalRevenue","GrossProfit"), 
         YMatrix, c
		 (1,1,2,2), 
         ClassNames=c("Class 1", "Class 2"), 
         main="ClassErrorbar of Q1 2018 for total revenue and gross profit",
         xlab="GrossProfit/TotalRevenue", 
         ylab="Median +- std", 
         WhiskerWidth = 1)
		 
#Option 2: numerical vector
ClassErrorbar(c(1,2), 
		 YMatrix,
		 c(1,1,2,2), 
         ClassNames=c("Class 1", "Class 2"), 
         main="ClassErrorbar of Q1 2018 for total revenue and gross profit",
         xlab="GrossProfit/TotalRevenue", 
         ylab="Median +- std", 
         WhiskerWidth = 1)

#Option 3: numerical vector + line
## Not run: 
#arbitrary data
Y_someOtherData=cbind(YMatrix,YMatrix,
YMatrix,YMatrix)
some_values=c(2,3,4,5,6,8,9,10)
ClassErrorbar(some_values, 
		 Y_someOtherData,
		 c(1,1,2,2), 
         ClassNames=c("Class 1", "Class 2"), 
         main="ClassErrorbar of Q1 2018 for total revenue and gross profit",
         xlab="GrossProfit/TotalRevenue", 
         ylab="Median +- std", 
         WhiskerWidth = 1)$ggobj+
geom_smooth(method="auto", se=F, fullrange=F, level=0.95)

## End(Not run)

Class MDplot for Data w.r.t. all classes

Description

Creates a Mirrored-Density plot w.r.t. to each class of a numerical vector of data.

Usage

ClassMDplot(Data, Cls, ColorSequence = DataVisualizations::DefaultColorSequence,

                         ClassNames = NULL, PlotLegend = TRUE,Ordering = "Columnwise",
                         
                         main = 'MDplot for each Class',
                         
                         xlab = 'Classes', ylab = 'PDE of Data per Class',
                         
                         Fill = 'darkblue', MinimalAmoutOfData=40,
                         
                         MinimalAmoutOfUniqueData=12,SampleSize=1e+05,...)

Arguments

Data

[1:n] Vector of the data to be plotted

Cls

[1:n] Vector of class identifiers of k clusters one number is the label of one cluster

ColorSequence

Optional: [1:k] vector, The sequence of colors used, Default: DataVisualizations::DefaultColorSequence

ClassNames

Optional: [1:k] named numerical vector, The names of the classes. Default: Class 1 - Class k with k beeing the number of classes

PlotLegend

Optional: Add a legent to plot. Default: TRUE)

Ordering

Optional: Ordering of Classes, please see MDplot for details)

main

Optional: Title of the plot. Default: MDplot for each Class

Fill

Optional: [1:k] Vector with the colors, the MD's are to be colored with. If only one value is given, all MD's are colored in the same color.

xlab

Optional: Title of the x axis. Default: "Classes"

ylab

Optional: Title of the y axis. Default: "Data"

MinimalAmoutOfData

Optional: numeric value defining a threshold. Below this threshold no density estimation is performed and a Jitter plot with a median line is drawn. Please see MDplot for details.

MinimalAmoutOfUniqueData

Optional: numeric value defining a threshold. Below this threshold no density estimation and statistical testing is performed and a Jitter plot is drawn. Only Data Science experts should change this value after they understand how the density is estimated (see [Ultsch, 2005]).

SampleSize

Optional: numeric value defining a threshold. Above this thresholdclass-wise uniform sampling of finite cases is performed in order to shorten computation time. If required, SampleSize=n can be set to omit this procedure.

...

Further arguments that are documented in MDplot except for OnlyPlotOutput which is always true.

Details

Further examples for the ClassMDplot can be found in https://md-plot.readthedocs.io/en/latest/application/example_application.html.

The Cls vector is reordered from lowest to highest number. The ClassNames vector and ColorSequence vectors are matched by this ordering of Cls, i.e. the lowest number gets the first color or class name.

Value

A List of

ClassData

The matrix [1:m,1:NoOfClasses] used to plot with the reordered Cls, rows are filled partly with NaN, m is the length of the number of data in largest class.

ggobject

The ggplot2 plot object

in mode invisible

Note

Function is still experimental because ColorSequence does not work yet, because we are unable to specify the colors in ggplot2. If someone knows a solution, please mail the maintainer of the package. Similar issue for PlotLegend.

Author(s)

Michael Thrun, Felix Pape

References

Thrun, M. C., Breuer, L., & Ultsch, A. : Knowledge discovery from low-frequency stream nitrate concentrations: hydrology and biology contributions, Proc. European Conference on Data Analysis (ECDA), Paderborn, Germany, 2018.

See Also

https://md-plot.readthedocs.io/en/latest/application/example_application.html

MDplot https://pypi.org/project/md-plot/

Examples

data(ITS)

#shortcut for example if AdaptGauss not installed
Classification = kmeans(ITS, centers = 2)$cluster

#better approach
#please download package from cran
#model=AdaptGauss::AdaptGauss(ITS)
#Classification=AdaptGauss::ClassifyByDecisionBoundaries(ITS,

#DecisionBoundaries = AdaptGauss::BayesDecisionBoundaries(model$Means,model$SDs,model$Weights))
ClassNames=c(1,2)
names(ClassNames)=c("Insert name \n of Class 1","Insert name \n  of Class 2")
ClassMDplot(ITS,Classification,ClassNames = ClassNames)

PDE Plot for all classes

Description

PDEplot the data for all classes, weights the pdf with priors

Usage

ClassPDEplot(Data, Cls, ColorSequence,

 ColorSymbSequence, PlotLegend = 1,

 SameKernelsAndRadius = 0, xlim, ylim, ...)

Arguments

Data

The Data to be plotted

Cls

Vector of class identifiers. Can be integers or NaN's, need not be consecutive nor positive

ColorSequence

Optional: the sequence of colors used, Default: DefaultColorSequence

ColorSymbSequence

Optional: the plot symbols used (theoretisch nicht notwendig, da erst wichtig, wenn mehr als 562 Cluster)

PlotLegend

Optional: add a legent to plot (default == 1)

SameKernelsAndRadius

Optional: Use the same PDE kernels and radii for all distributions (default == 0)

xlim

Optional: range of the x axis

ylim

Optional: range of the y axis

...

further arguments passed to plot

Value

Kernels of the Pareto density estimation in mode invisible

Author(s)

Michael Thrun

Examples

data(ITS)
#please download package from cran
#model=AdaptGauss::AdaptGauss(ITS)
#Classification=AdaptGauss::ClassifyByDecisionBoundaries(ITS,

#DecisionBoundaries = AdaptGauss::BayesDecisionBoundaries(model$Means,model$SDs,model$Weights))

DataVisualizations::ClassPDEplot(ITS,Classification)$ggobject

Create PDE plot for all classes with maximum likelihood

Description

PDEplot the data for allclasses, weight the Plot with 1 (= maximum likelihood)

Usage

ClassPDEplotMaxLikeli(Data, Cls, ColorSequence = DataVisualizations::DefaultColorSequence,

 ClassNames, PlotLegend = TRUE, MinAnzKernels = 0,PlotNorm,

 main = "Pareto Density Estimation (PDE)",

 xlab = "Data", ylab = "ParetoDensity", xlim, ylim, lwd=1, ...)

Arguments

Data

The Data to be plotted

Cls

Vector of class identifiers. Can be integers or NaN's, need not be consecutive nor positive

ColorSequence

Optional: the sequence of colors used, Default: DefaultColorSequence

ClassNames

Optional: the names of the classes to be displayed in the legend

PlotLegend

Optional: add a legent to plot (default == 1)

MinAnzKernels

Optional: Minimum number of kernels

PlotNorm

Optional: ==1 => plot Normal distribuion on top , ==2 = plot robust normal distribution,; default: PlotNorm= 0

main

Optional: Title of the plot

xlab

Optional: title of the x axis

ylab

Optional: title of the y axis

xlim

Optional: area of the x-axis to be plotted

lwd

Optional: area of the y-axis to be plotted

ylim

numerical scalar defining the width of the lines

...

further arguments passed to plot

Value

Kernels

Kernels of the distributions

ClassParetoDensities

Pareto densities for classes

ggobject

ggplot2 plot object. This should be used to further modify the plot

Author(s)

Felix Pape

References

Aubert, A. H., Thrun, M. C., Breuer, L., & Ultsch, A. : Knowledge discovery from high-frequency stream nitrate concentrations: hydrology and biology contributions, Scientific reports, Nature, Vol. 6(31536), pp. doi 10.1038/srep31536, 2016.

Examples

data(ITS)
#model=AdaptGauss::AdaptGauss(ITS)
##please download package from cran
#Classification=AdaptGauss::ClassifyByDecisionBoundaries(ITS,

#DecisionBoundaries = AdaptGauss::BayesDecisionBoundaries(model$Means,model$SDs,model$Weights))

DataVisualizations::ClassPDEplotMaxLikeli(ITS,Classification)$ggobject

Classplot

Description

Allows to plot one time series or feauture with a classification as a labeled scatter plot with a line. The colors are the labels defined by the classification.

Usage

Classplot(X, Y, Cls, Plotter,Names = NULL, na.rm = FALSE, 

xlab = "X", ylab = "Y", main = "Class Plot", Colors = NULL,

Size = 8,PointBorderCol="black",

LineColor = NULL, LineWidth = 1, LineType  = NULL, 

Showgrid  = TRUE, pch,  AnnotateIt = FALSE, SaveIt = FALSE, 

Nudge_x_Names = 0, Nudge_y_Names = 0, Legend = "", SmallClassesOnTop = TRUE,

...)

Arguments

X

[1:n] numeric vector or time

Y

[1:n] numeric vector of feature

Cls

[1:n] numeric vector of k classes, if not set per default every point is in first class

Names

[1:n] character vector of k classes, if not set per default Cls is used, if set, names the legend and the points

na.rm

Function may not work with non finite values. If these cases should be automatically removed, set parameter TRUE

xlab

Optional, string for xlabel

ylab

Optional, string for ylabel

main

Optional, string for title of plot

Colors

Optional, [1;k] string defining the k colors, one per class

AnnotateIt

Optional, in case of Plotter==ggplot and given Names annotates each point if TRUE

Size

Optional, size of points, beware: default is appropriate for "plotly", or "native" but should smaller for "ggplot"

PointBorderCol

Optional, string, color of the dot outline for "plotly" for "ggplot". If FALSE and Plotter="ggplot" or Plotter="plotly", no borders for points which is useful if many points overlap.

LineColor

Optional, name of color, in plotly then all points are connected by a curve,

in ggplot2 all points of one class ae connected by a curve of the color the class

LineWidth

Optional, number defining the width of the curve (plotly only)

LineType

Optional, string defining the type of the curve in plotly only, "dot", "dash", "-"

for ggplot2: just set =1 here and then the curve is plotted

Showgrid

Optional, boolean (plotly only)

Plotter

Optional, either "ggplot" (default if Names given), "plotly" (default if no Names given), or "native"

pch

[1:n] numeric vector of length n of the cases of Cls for the k classes. It defines the symbols to use, for native Plotter or ggplot, usally k can be in a range from zero to 25

SaveIt

Optional, boolean, if true saves plot as html (plotly) or png (ggplot2)

Nudge_x_Names

Optional, numerical scalar, for Plotter "ggplot" only, if Names are set, moves them consistently respective to x-axis within units of x-axis

Nudge_y_Names

Optional, numerical scalar, for Plotter "ggplot" only, if Names are set, moves them consistently respective to y-axis within units of y-axis

SmallClassesOnTop

Optional, boolean, decide if small classes should be plotted on top for visibility (default setting) or not.

Legend

Optional, if argument is not missing, character string defining the title of the legend which automatically enables the legend

...

Further arguments for ggplot2::ggplot,or plotly::plot_ly, or plot (except "pch"" and "type") depending on Plotter

Details

The mapping of colors to the labels of Cls is consecutive, i.e., the label with the smallest value in Cls gets the first color in Colors. The Colors are plotted in order from label with the highest number of points to the label with the lowest number of points beeing on top.

Default is "plotly" if Names are NULL. However, ggplot2 is preferable in case that Names parameter is used because overlapping text labels are avoided. In that case the default is "ggplot". Note that ggplot2 options are currently slightly restricted.

For example, the function is usefull to see if temporal clustering has time dependent variations and for Hidden Markov Models (see Mthrun/RHmm on GitHub).

Value

plotly object or ggplot2 objected depending on Plotter

Author(s)

Michael Thrun

See Also

DualaxisClassplot

Examples

data(Lsun3D)
Classplot(Lsun3D$Data[,1],Lsun3D$Data[,2],Lsun3D$Cls)

#ggplot 2 with different symbols
  Classplot(
    Lsun3D$Data[, 1],
    Lsun3D$Data[, 2],
    Lsun3D$Cls,
    Plotter = "ggplot2",
    Size = 3,
    pch = Lsun3D$Cls + 5
  )

#plotly with line
data(Lsun3D)
Classplot(Lsun3D$Data[,1],Lsun3D$Data[,2],Lsun3D$Cls,
LineType="-",LineColor = "green")

#ggplot2 with annotations
data(Lsun3D)
ind=sample(1:nrow(Lsun3D$Data),20)
Classplot(Lsun3D$Data[ind,1],Lsun3D$Data[ind,2],Lsun3D$Cls[ind],
Names = rownames(Lsun3D$Data)[ind],Size =1,
Plotter = "ggplot2",AnnotateIt = TRUE)



#ggplot2 with labels and legend per class
data(Lsun3D)
Classplot(Lsun3D$Data[,1],Lsun3D$Data[,2],Lsun3D$Cls,
Names = paste0("C",Lsun3D$Cls),Size =2,Legend ="Classes")

Combine vectors of various lengths

Description

Combine arbitrary vectors of data, filling in missing rows with NaN

Usage

CombineCols(...,na.rm=FALSE)

Arguments

...

d vectors of arbitrary lengths, see example

na.rm

boolean: FALSE: fills with NaN TRUE: filles with zeros

Details

Robust alternative to cbind that fills missing values with nan instead of extending length of vector by duplicating elements

Value

matrix of dimensionality of n x d with n beeing the length of the longest vector and d the number of vectors given as input

Note

special application by MCT of rowr cbind.fill which is now not on CRAN anymore

Author(s)

Craig Varrichio

See Also

CombineRows

Examples

CombineCols(c(1,2,3),c(1),c(2,3))

Combine matrices of various lengths

Description

Combine arbitrary matrices of data, filling in missing columns with NaN

Usage

CombineRows(...,na.rm=FALSE)

Arguments

...

First argument is a matrix usually with named columns, thereafter either matrices or d vectors of arbitrary lengths, see example

na.rm

boolean: FALSE: fills with NaN TRUE: filles with zeros

Details

Robust alternative to rbind that fills missing values with #NaN, tries to match given column names if matrices are inserted otherwise fills up the missing columns at the end.

The first argument has to be a matrix. It is assumed that this matrix has to be filled up and other arguments or not of bigger size than d columns. Otherwiese the further elements stored in columns >d are ignored.

Value

matrix of dimensionality of n x d with n beeing the number of rows of the first argument and d the number columns of the first argument given as input

Author(s)

Michael Thrun

See Also

CombineRows

Examples

matrix_pattern=cbind(c(1,2,3),c(4,5,6),c(7,8,9))

CombineRows(matrix_pattern,c(1),c(2,3))


CombineRows(matrix_pattern,cbind(c(1,2,3),c(4,5,6)))

Crosstable plot

Description

Presents a heatmap with values and a cross table of given Data matrix of two features and a bin width or percentualized values. In this approach the bin width is fixes. A more general way to approach this is the kernel density estimation plot of PDEscatter.

Usage

Crosstable(Data, xbins = seq(0, 100, 5), ybins = xbins, 

NormalizationFactor = 1, PlotIt = TRUE, main='Cross Table',

PlotText=TRUE,TextDigits=0,TextProbs=c(0.05,0.95))

Arguments

Data

[1:n,1:2] matrix of two features from which the cross table should be generated from

xbins

[1:k] start of k bins as a vector generated with seq of the first feature of data. Default setting assumes percentiled values between zero and 100.

ybins

[1:k] start of k bins as a vector generated with seq of the second feature of data. Normally the same for both features, other settings are only possible if the length k is equal.

NormalizationFactor

Optional, Data feautures can be seen as regular time series, e.g. 1 measurement for a minute, in this case it is useful to normalize the output, e.g. to hours, then NormalizationFactor=60

PlotIt

Optional, Plots the heatmap if TRUE. The first feature is on the x-axis (left to right) and the second on y-axis (bottom to top).

main

In case of for PlotIt=TRUE: title of plot, see title

PlotText

In case of for PlotIt=TRUE: Default TRUE: plots text in heatmap with the values of the crosstable

TextDigits

In case of for TextDigits=TRUE: integer indicating the number of decimal places to use in round.

TextProbs

In case of for TextDigits=TRUE: [1:2] numeric vector of two probabilities defining the thresholds for white text to grey text and grey text to black text, e.g. below the first threshold (Default 0.05) all values (5% of values) will be printed in white because the lowest values of the heatmap are blue. The second value of 0.95 works well if cross table has many zeros; uses quantile internally.

Details

The interval in each bin is closed to the left and opened to the right. The cross table can be seen as a two-dimensional histogram. The idea to add histograms to the table is taken from [Charpentier. 2014].

Value

The cross table in invisible mode which depicts the number of values (frequency) in an specific range with regard to two features.

The first feature is on the x-axis (left to right), and the second on y-axis (top to bottom) contrary to the plot where it is bottom to top.

Note

For non percentiled values the PlotText part does not seem always to work, but I currently dont know why the text does not always overlap with the heatmap.

Author(s)

Michael Thrun

References

[Charpentier. 2014] Charpentier, Arthur, ed. Computational actuarial science with R. CRC Press, 2014.

See Also

table, image, PDEscatter

Examples

data(ITS)
data(MTY)
#simple but not a good transformation
Data=(cbind(ITS/max(ITS),MTY/max(MTY)))*100
#choice for bins could be better
Crosstable(Data)

Default color sequence for plots

Description

Defines the default color sequence for plots made within the Projections package.

Usage

data("DefaultColorSequence")

Format

A vector with 562 different strings describing colors for plots.


Contour plot of densities

Description

Density estimation (PDE) [Ultsch, 2005] or "SDH" [Eilers/Goeman, 2004] used for a density contour plot.

Usage

DensityContour(X,Y, DensityEstimation="SDH", 

SampleSize, na.rm=FALSE,PlotIt=TRUE,
                              
NrOfContourLines=20,Plotter='ggplot', DrawTopView = TRUE,
                              
xlab, ylab, main="DensityContour",
                              
xlim, ylim, Legendlab_ggplot="value",

AddString2lab="",NoBinsOrPareto=NULL,...)

Arguments

X

Numeric vector [1:n], first feature (for x axis values)

Y

Numeric vector [1:n], second feature (for y axis values)

DensityEstimation

"SDH" is very fast but maybe not correct, "PDE" is slow but proably more correct, third alternativ is the typical R density estimation with "kde2d" which is sensitive to parameters

SampleSize

Numeric, positiv scalar, maximum size of the sample used for calculation. High values increase runtime significantly. The default is that no sample is drawn

na.rm

Function may not work with non finite values. If these cases should be automatically removed, set parameter TRUE

PlotIt

TRUE: plots with function call

FALSE: Does not plot, plotting can be done using the list element Handle

NrOfContourLines

Numeric, number of contour lines to be drawn. 20 by default.

Plotter

String, name of the plotting backend to use. Possible values are: "ggplot", "plotly". Default: ggplot

DrawTopView

Boolean, True means contur is drawn, otherwise a 3D plot is drawn. Default: TRUE

xlab

String, title of the x axis. Default: "X", see plot() function

ylab

String, title of the y axis. Default: "Y", see plot() function

main

string, the same as "main" in plot() function

xlim

see plot() function

ylim

see plot() function

Legendlab_ggplot

String, in case of Plotter="ggplot" label for the legend. Default: "value"

AddString2lab

adds the same string of information to x and y axis label, e.g. usefull for adding SI units

NoBinsOrPareto

Density specifc parameters, for PDEscatter(ParetoRadius) or SDH (nbins)) or kde2d(bins)

...

further plot arguments

Details

The DensityContour function generates the density of the xy data as a z coordinate. Afterwards xyz will be plotted either as a contour plot or a 3d plot. It assumens that the cases of x and y are mapped to each other meaning that a cbind(x,y) operation is allowed. This function plots the Density on top of a scatterplot. Variances of x and y should not differ by extreme numbers, otherwise calculate the percentiles on both first. If DrawTopView=FALSE only the plotly option is currently available. If another option is chosen, the method switches automatically there.

PlotIt=FALSE is usefull if one likes to perform adjustements like axis scaling prior to plotting with ggplot2 or plotly.

Value

List of:

X

Numeric vector [1:m],m<=n, first feature used in the plot or the kernels used

Y

Numeric vector [1:m],m<=n, second feature used in the plot or the kernels used

Densities

Number of points within the ParetoRadius of each point, i.e. density information

Handle

Handle of the plot object

Note

MT contributed with several adjustments

Author(s)

Felix Pape

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, (Ultsch, A. & Huellermeier, E. Eds., 10.1007/978-3-658-20540-9), Doctoral dissertation, Heidelberg, Springer, ISBN: 978-3658205393, 2018.

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, In Baier, D. & Werrnecke, K. D. (Eds.), Innovations in classification, data science, and information systems, (Vol. 27, pp. 91-100), Berlin, Germany, Springer, 2005.

[Eilers/Goeman, 2004] Eilers, P. H., & Goeman, J. J.: Enhancing scatterplots with smoothed densities, Bioinformatics, Vol. 20(5), pp. 623-628. 2004.

Examples

#taken from [Thrun/Ultsch, 2018]
data("ITS")
data("MTY")
Inds=which(ITS<900&MTY<8000)
plot(ITS[Inds],MTY[Inds],main='Bimodality is not visible in normal scatter plot')

DensityContour(ITS[Inds],MTY[Inds],DensityEstimation="SDH",xlab = 'ITS in EUR',

ylab ='MTY in EUR' ,main='Smoothed Densities histogram indicates Bimodality' )

DensityContour(ITS[Inds],MTY[Inds],DensityEstimation="PDE",xlab = 'ITS in EUR',

ylab ='MTY in EUR' ,main='PDE indicates Bimodality' )

Scatter plot with densities

Description

Density estimation is performed by (PDE) [Ultsch, 2005] or "SDH" [Eilers/Goeman, 2004] and visualized in a density scatter plot [Brinkmann et al., 2023] in which the points are colored by their density.

Usage

DensityScatter(X,Y,DensityEstimation="SDH",

Type="DDCAL", Plotter = "native",Marginals = FALSE,

SampleSize,na.rm=FALSE, xlab, ylab, 

main="DensityScatter", AddString2lab="",
                        
xlim, ylim,NoBinsOrPareto=NULL,...)

Arguments

X

Numeric vector [1:n], first feature (for x axis values)

Y

Numeric vector [1:n], second feature (for y axis values)

DensityEstimation

(Optional), "SDH" is very fast but maybe not correct, "PDE" is slow but proably more correct, third alternativ is the typical R density estimation with "kde2d" which is sensitive to parameters

Type

(Optional), "DDCAL" uses a new density to point color matching by DDCAL algorithm [Lux/Rinderle-Ma, 2023] , "native" uses a simple density to point color matching

Plotter

in case of Type="DDCAL", (Optional) String, name of the plotting backend to use. Possible values are: "native","plotly", or "ggplot2"

Marginals

(Optional) Boolean, if TRUE the marginal distributions of X and Y will be plotted together with the 2D density of X and Y. Default is FALSE

SampleSize

(Optional), Numeric, positiv scalar, maximum size of the sample used for calculation. High values increase runtime significantly. The default is that no sample is drawn

na.rm

(Optional), Function may not work with non finite values. If these cases should be automatically removed, set parameter TRUE

xlab

(Optional), String, title of the x axis. Default: "X", see plot() function

ylab

(Optional), String, title of the y axis. Default: "Y", see plot() function

main

(Optional), string, the same as "main" in plot() function

AddString2lab

(Optional), adds the same string of information to x and y axis label, e.g. usefull for adding SI units

xlim

(Optional), in case of Type="natuive", see plot() function

ylim

in case of Type="natuive", see plot() function

NoBinsOrPareto

(Optional), in case of Type="natuive", Density specifc parameters, for PDEscatter(ParetoRadius) or SDH (nbins)) or kde2d(bins)

...

(Optional), further arguments either to ScatterDenstiy::DensityScatter.DDCAL or to plot()

Details

The DensityScatter function generates the density of the xy data as a z coordinate. Afterwards xy points will be plotted as a scatter plot, where the z values defines the coloring of the xy points. It assumens that the cases of x and y are mapped to each other meaning that a cbind(x,y) operation is allowed. This function plots the Density on top of a scatterplot. Variances of x and y should not differ by extreme numbers, otherwise calculate the percentiles on both first.

Value

List of:

X

Numeric vector [1:m],m<=n, first feature used in the plot or the kernels used

Y

Numeric vector [1:m],m<=n, second feature used in the plot or the kernels used

Densities

Number of points within the ParetoRadius of each point, i.e. density information

Note

MT contributed with several adjustments

Author(s)

Felix Pape

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, (Ultsch, A. & Huellermeier, E. Eds., 10.1007/978-3-658-20540-9), Doctoral dissertation, Heidelberg, Springer, ISBN: 978-3658205393, 2018.

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, In Baier, D. & Werrnecke, K. D. (Eds.), Innovations in classification, data science, and information systems, (Vol. 27, pp. 91-100), Berlin, Germany, Springer, 2005.

[Eilers/Goeman, 2004] Eilers, P. H., & Goeman, J. J.: Enhancing scatterplots with smoothed densities, Bioinformatics, Vol. 20(5), pp. 623-628. 2004

[Lux/Rinderle-Ma, 2023] Lux, M. & Rinderle-Ma, S.: DDCAL: Evenly Distributing Data into Low Variance Clusters Based on Iterative Feature Scaling, Journal of Classification vol. 40, pp. 106-144, 2023.

[Brinkmann et al., 2023] Brinkmann, L., Stier, Q., & Thrun, M. C.: Computing Sensitive Color Transitions for the Identification of Two-Dimensional Structures, Proc. Data Science, Statistics & Visualisation (DSSV) and the European Conference on Data Analysis (ECDA), p.109, Antwerp, Belgium, July 5-7, 2023.

Examples

#taken from [Thrun/Ultsch, 2018]
data("ITS")
data("MTY")
Inds=which(ITS<900&MTY<8000)
plot(ITS[Inds],MTY[Inds],main='Bimodality is not visible in normal scatter plot')

DensityScatter(ITS[Inds],MTY[Inds],DensityEstimation="SDH",xlab = 'ITS in EUR',

ylab ='MTY in EUR' ,main='Smoothed Densities histogram indicates Bimodality' )

DensityScatter(ITS[Inds],MTY[Inds],DensityEstimation="PDE",xlab = 'ITS in EUR',

ylab ='MTY in EUR' ,main='PDE indicates Bimodality' )

DiagnosticAbility4Classifiers

Description

DiagnosticAbility4Classifiers as applied in [...].

Usage

DiagnosticAbility4Classifiers(TrueCondition_Cls, ManyPredictedCondition_Cls,

NamesOfConditions = NULL, PlotType = "PRC", xlab = "True Positive Rate",

ylab = "False Positive Rate", main = "ROC Space",

Colors, LineColor = NULL, Size = 8, LineWidth = 1,

LineType = NULL, Showgrid = TRUE, SaveIt = FALSE)

Arguments

TrueCondition_Cls

[1:n] numeric vector of k classes (true classification), preferably of the testset

ManyPredictedCondition_Cls

[1:n,1:c] every col c is a Cls of one specific condition of the classifier trying to reproduce the classification (preferably on a test set)

NamesOfConditions

[1:c] character vector of c conditions, sets names of legend and the points

PlotType

possible are 'ROC':Receiver operating characteristic. 'PRC': Precision Recall, and 'SenSpec':Sensitivity-Specifity Plot

xlab

Optional, string

ylab

Optional, string

main

Optional, string

Colors

Optional, string

LineColor

Optional, name of color, then all points are connected by a curve

Size

Optional, number defining the Size of the curve

LineWidth

Optional, number defining the width of the curve

LineType

Optional, string defining the type of the curve

Showgrid

Optional, boolean

SaveIt

Optional, boolean, if true saves plot as html

Details

For unbalanced binary classes PRC should be preferred and not ROC [Saito/Rehmsmeier, 2016].

Value

If it is a LIST, use

Plot

plotly handler

X

[1:c] vector of xaxis values

Y

[1:c] vector of y axis values

Note

Currently only for binary classifiers developed

Author(s)

Michael Thrun

References

[|] :Determination of CD43 and CD200 surface expression improves accuracy of B-cell lymphoma immunophenotyping, 2020.

[Saito/Rehmsmeier, 2016] Saito, Takaya and Rehmsmeier, Marc: The Precision-Recall Plot Is More Informative than the ROC Plot When Evaluating Binary Classifiers on Imbalanced Datasets, PlosOne, https://doi.org/10.1371/journal.pone.0118432, 2016.

See Also

Classplot

Examples

#TODo

Plot a classificated world map

Description

This function plots a world map where the single countries get colored differently by using a classification

Arguments

CountryCode

Vector of Countrys belonging to the Cls

Cls

Classes belonging to the Countries from CountryCode

JoinCode

System that is used for the CountryCodes. Possible are: "ISO3", "UN"

Title

Title that will be written above the map

Colors

Vector that colors for classes will be selected from

Value

a plot

Author(s)

Florian Lerch


Dualaxis Classplot

Description

Allows to plot two time series or features with one or two classification(a) as labeled scatter plots. The colors are the labels defined by the classification. Usefull to see if temporal clustering has time dependent variations and for Hidden Markov Models (see Mthrun/RHmm on GitHub).

Usage

DualaxisClassplot(X, Y1, Y2, Cls1,

Cls2, xlab = "X", y1lab = "Y1", y2lab = "Y2",

main = "Dual Axis Class Plot", Colors, Showgrid = TRUE, SaveIt = FALSE)

Arguments

X

[1:n] numeric vector or time

Y1

[1:n] numeric vector of feauture

Y2

[1:n] numeric vector of feauture

Cls1

[1:n] numeric vector defining a classification of k1 classes

Cls2

Optional, [1:n] numeric vector defining a classification of k2 classes for Y2

xlab

Optional, string

y1lab

Optional, string

y2lab

Optional, string

main

Optional, string

Colors

[1:(k1+k2)] Colornames

Showgrid

Optional, boolean

SaveIt

Optional, boolean

Value

plotly object

Author(s)

Michael Thrun

See Also

Classplot

Examples

##ToDo

DualaxisLinechart

Description

A line chart with dual axisSS

Usage

DualaxisLinechart(X, Y1, Y2, xlab = "X", 

y1lab = "Y1", y2lab = "Y2", main = "Dual Axis Line Chart",

cols = c("black", "blue"),Overlaying="y", SaveIt = FALSE)

Arguments

X

[1:n] vector, both lines require the same xvalues, e.g. the time of the time series, POSIXlt or POSIXct are accepted

Y1

[1:n] vector of first line

Y2

[1:n] vector of second line

xlab

Optional, string for xlabel

y1lab

Optional, string for first ylabel

y2lab

Optional, string for second ylabel

main

Optional, title of plot

cols

Optional, color of two lines

Overlaying

Change only default in case of using subplot

SaveIt

Optional, default FALSE; TRUE if you want to save plot as html in getwd() directory

Details

enables to visualize to lines in one plot overlaying them using ploty (e.g. two time series with two ranges of values)

Value

plotly object

Author(s)

Michael Thrun

Examples

#subplot renames the numbering of subsequent plots
y1=runif(100,0,1)
y2=rnorm(100,m=5,s=1)
DualaxisLinechart(1:100, y1, y2,main="Random Time series")


y1=runif(100,0,1)
y2=(1:100*3+4)*runif(100,0,1)
p1=DualaxisLinechart(1:100, y1, y2,main="Random Time series",Overlaying="y2")

y3=1:100*(-2)+4
y4=rnorm(100,m=0,s=2)
p2=DualaxisLinechart(1:100, y3, y4,main="Random Time series",Overlaying="y4")
plotly::subplot(p1,p2)

estimateDensity2D

Description

Estimates densities for two-dimensional data with the given estimation type

Usage

estimateDensity2D(X, Y, DensityEstimation = "SDH",

SampleSize, na.rm = FALSE, NoBinsOrPareto = NULL)

Arguments

X

[1:n] numerical vector of first feature

Y

[1:n] numerical vector of second feature

DensityEstimation

Either "PDE","SDH" or "kde2d"

SampleSize

Sample Size in case of big data

na.rm

Function may not work with non finite values. If these cases should be automatically removed, set parameter TRUE

NoBinsOrPareto

Density specifc parameters, for PDEscatter(ParetoRadius) or SDH (nbins)) or kde2d(bins)

Details

Each two-dimensional data point is defined by its corresponding X and Y value.

Value

List V with

X

[1:m] numerical vector of first feature, m<=n depending if all values are finite an na.rm parameter

Y

[1:m] numerical vector of second feature, m<=n depending if all values are finite an na.rm parameter

Densities

the density of each two-dimensional data point

Author(s)

Luca Brinkman and Michael Thrun

References

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, In Baier, D. & Werrnecke, K. D. (Eds.), Innovations in classification, data science, and information systems, (Vol. 27, pp. 91-100), Berlin, Germany, Springer, 2005.

[Eilers/Goeman, 2004] Eilers, P. H., & Goeman, J. J.: Enhancing scatterplots with smoothed densities, Bioinformatics, Vol. 20(5), pp. 623-628. 2004

Examples

X=runif(100)
Y=rnorm(100)
#V=estimateDensity2D(X,Y)

The fan plot

Description

The better alternative to the pie chart represents amount of values given in data.

Usage

Fanplot(Datavector,Names,Labels,MaxNumberOfSlices,main='',col,
MaxPercentage=FALSE,ShrinkPies=0.05,Rline=1.1, lwd=2,LabelCols="black",...)

Arguments

Datavector

[1:n] a vector of n non unique values

Names

Optional, [1:k] names to search for in Datavector, if not set unique of Datavector is calculated.

Labels

Optional, [1:k] Labels if they are specially named, if not Names are used.

MaxNumberOfSlices

Default is k, integer value defining how many labels will be shown. Everything else will be summed up to Other.

main

Optional, title below the fan pie, see plot

col

Optional, the default are the first [1:k] colors of the default color sequence used in this package, otherwise a character vector of [1:k] specifying the colors analog to plot

MaxPercentage

default FALSE; if true the biggest slice is 100 percent instead of the biggest procentual count

ShrinkPies

Optional, distance between biggest and smallest slice of the pie

Rline

Optional, the distance between text and pie is defined here as the length of the line in numerical numbers

lwd

Optional, The line width, a positive number, defaut is 2

LabelCols

Color of labels

...

Further arguments to fan.plot like circumferential positions for the labels labelpos or additional arguments passed to polygon

Details

A normal pie plot is dificult to interpret for a human observer, because humans are not trained well to observe angles [Gohil, 2015, p. 102]. Therefore, the fan plot is used. As proposed in [Gohil 2015] the fan.plot() of the plotrix package is used to solve this problem. If Number of Slices is higher than MaxNumberOfSlices then ABCanalysis is applied (see [Ultsch/Lotsch, 2015]) and group A chosen. If Number of Slices in group A is higher than MaxNumberOfSlices, then the most important ones out of group A are chosen. If MaxNumberOfSlices is higher than Slices in group A, additional slices are shown depending on the percentage (from high to low).

Color sequence is automatically shortened to the MaxNumberOfSlices used in the fan plot.

Value

silent output by calling invisible of a list with

Percentages

[1:k] percent values visualized in fanplot

Labels

[1:k] see input Labels, only relevant ones

Author(s)

Michael Thrun

References

[Gohil, 2015] Gohil, Atmajitsinh. R data Visualization cookbook. Packt Publishing Ltd, 2015.

[Ultsch/Lotsch, 2015] Ultsch. A ., Lotsch J.: Computed ABC Analysis for Rational Selection of Most Informative Variables in Multivariate Data, PloS one, Vol. 10(6), pp. e0129767. doi 10.1371/journal.pone.0129767, 2015.

See Also

fan.plot Piechart

Examples

data(categoricalVariable)
Fanplot(categoricalVariable)

Fundamental Data of the 1st Quarter in 2018

Description

This dataset was extracted out of Yahoo finance and was investigated in [Thrun et al., 2019] and clustered in [Thrun, 2019].

Usage

data("FundamentalData_Q1_2018")

Format

The format is: List of 3 $ Data :'data.frame': 269 obs. of 45 variables: ..$ TotalRevenue : num [1:269] 3779000 78225 48220 63726 3084 ... ..$ CostofRevenue : num [1:269] 2348000 60835 26174 35203 882 ... ..$ GrossProfit : num [1:269] 1431000 17390 22046 28523 2202 ... ..$ SellingGeneralandAdministrative : num [1:269] 459000 NaN 15162 17072 2005 ... ..$ Others : num [1:269] -3000 10272 -52 3131 1784 ... ..$ TotalOperatingExpenses : num [1:269] 2872000 73833 41284 56787 5081 ... ..$ OperatingIncomeorLoss : num [1:269] 907000 4392 6936 6939 -1997 ... ..$ TotalOtherIncomeDIVxpensesNet : num [1:269] -28000 -344 1 -210 -240 ... ..$ EarningsBeforeInterestandTaxes : num [1:269] 907000 4392 6936 6939 -1997 ... ..$ InterestExpense : num [1:269] -20000 -415 NaN -243 -238 ... ..$ IncomeBeforeTax : num [1:269] 879000 4048 6937 6729 -2237 ... ..$ IncomeTaxExpense : num [1:269] 233000 1365 2188 1896 7 ... ..$ NetIncomeFromContinuingOps : num [1:269] 646000 2683 4749 4833 -2244 ... ..$ NetIncome_x : num [1:269] 644000 2817 4645 4833 -2244 ... ..$ NetIncome : num [1:269] 644000 2817 4645 4833 -2244 ... ..$ CashAndCashEquivalents : num [1:269] 926000 29047 45911 94859 11217 ... ..$ NetReceivables : num [1:269] 2527000 46171 20774 151952 2774 ... ..$ Inventory : num [1:269] 2011000 471 NaN 10572 8924 ... ..$ TotalCurrentAssets : num [1:269] 5674000 80224 68061 267187 25989 ... ..$ LongTermInvestments : num [1:269] 234000 450 NaN 4155 872 ... ..$ PropertyPlantandEquipment : num [1:269] 4216000 14561 3093 32247 7073 ... ..$ IntangibleAssets : num [1:269] 78000 40706 3975 6169 125 ... ..$ OtherAssets : num [1:269] 810000 8224 1091 2978 13310 ... ..$ DeferredLongTermAssetCharges : num [1:269] 759000 684 1091 784 1405 ... ..$ TotalAssets : num [1:269] 11262000 167807 83155 351220 47369 ... ..$ AccountsPayable : num [1:269] 1442000 10567 1698 17316 1386 ... ..$ ShortDIVurrentLongTermDebt : num [1:269] 1275000 30192 NaN 26668 917 ... ..$ OtherCurrentLiabilities : num [1:269] 1064000 36942 22781 92297 2659 ... ..$ TotalCurrentLiabilities : num [1:269] 2577000 54430 24479 114210 4299 ... ..$ OtherLiabilities : num [1:269] 1795000 19435 6876 29347 2018 ... ..$ TotalLiabilities : num [1:269] 5576000 97136 31355 165628 6980 ... ..$ CommonStock : num [1:269] 198000 14946 5198 15250 28644 ... ..$ RetainedEarnings : num [1:269] NaN 44030 34767 40374 -8965 ... ..$ TreasuryStock : num [1:269] 5455000 11686 NaN 129968 20710 ... ..$ OtherStockholderEquity : num [1:269] 5455000 11686 NaN 129968 20710 ... ..$ TotalStockholderEquity : num [1:269] 5653000 70662 51212 185592 40389 ... ..$ NetTangibleAssets : num [1:269] 5325000 6314 40302 140939 40264 ... ..$ Depreciation : num [1:269] 156000 2728 331 1381 410 ... ..$ AdjustmentsToNetIncome : num [1:269] 216000 1911 116 2912 39 ... ..$ ChangesInOtherOperatingActivities : num [1:269] -20000 -2174 -829 NaN 428 ... ..$ TotalCashFlowFromOperatingActivities : num [1:269] 452000 7349 4274 -8241 -1367 ... ..$ CapitalExpenditures : num [1:269] -88000 -966 -1778 -2067 -155 ... ..$ TotalCashFlowsFromInvestingActivities: num [1:269] 30000 -879 -1766 -2746 -484 ... ..$ TotalCashFlowsFromFinancingActivities: num [1:269] -789000 -6660 -21867 -961 -204 ... ..$ ChangeInCashandCashEquivalents : num [1:269] -306000 -215 2508 -11842 -2062 ... $ Names: chr [1:269, 1:6] "1COV" "A1OS" "AAD" "AAG" ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:6] "Key" "ISIN" "Company" "Sector" ... $ Cls : num [1:269] 1 1 1 1 2 1 1 1 3 1 ...

Details

Stocks are selected by the German Prime standard accoridingly to the "Names" data frame. Fundamental Data with missing values is stored in "Data". The rownames of "Data" have the same Key as the first row of "Names" which is the trading symbol. "Cls" provides the clustering as a numerical vector of 1:k classes performed by Databionic Swarm in [Thrun, 2019].

Source

Yahoo finance

References

Thrun, M. C., : Knowledge Discovery in Quarterly Financial Data of Stocks Based on the Prime Standard using a Hybrid of a Swarm with SOM, in Verleysen, M. (Ed.), European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN), Vol. 27, pp. 397-402, Ciaco, ISBN: 978-287-587-065-0, Bruges, Belgium, 2019.

[Thrun et al., 2019] Thrun, M. C., Gehlert, Tino, & Ultsch, A. : Analyzing the Fine Structure of Distributions, arXiv:1908.06081, 2019.

Examples

data(FundamentalData_Q1_2018)
## maybe str(FundamentalData_Q1_2018) ; plot(FundamentalData_Q1_2018) ...

GermanPostalCodesShapes

Description

GermanPostalCodesShapes

Usage

data("GermanPostalCodesShapes")

Details

GermanPostalCodesShapes

Source

You could read https://www.r-bloggers.com/case-study-mapping-german-zip-codes-in-r/, if you want to change the map.

Examples

data(GermanPostalCodesShapes)
str(GermanPostalCodesShapes)

Google Maps with marked coordinates

Description

Google Maps with marked coordinates.

Usage

GoogleMapsCoordinates(Longitude,Latitude,Cls=rep(1,length(Longitude)),
zoom=3,location= c(mean(Longitude),mean(Latitude)),stroke=1.7,size=6,sequence)

Arguments

Longitude

sphaerischer winkel der Kugeloberflaeche, coord 1

Latitude

sphaerischer winkel der Kugeloberflaeche, coord 2

Cls

Vorklassification/Clusterung

zoom

map zoom, an integer from 3 (continent) to 21 (building), default value 10 (city). openstreetmaps limits a zoom of 18, and the limit on stamen maps depends on the maptype. "auto" automatically determines the zoom for bounding box specifications, and is defaulted to 10 with center/zoom specifications. maps of the whole world currently not supported

location

Optional, default: c(mean(Longitude),mean(Latitude); an address, longitude/latitude pair (in that order), or left/bottom/right/top bounding box

stroke

Optional, plotting parameter, dicke der linien der coordiantensymbole

size

Optional, plotting parameter, groesse der koordinatensymbole

sequence

Optional, vector of length of number of clusers with numbers indicating the plotting symbols and colors to use

Details

This plot was used in [Thrun, 2018, p. 135].

Value

ggobject()

Note

requires an Internet connection, requires an API key of Google. See ?ggmap::register_google for details.

Author(s)

Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20539-3, Heidelberg, 2018.


Heatmap for Clustering

Description

Heatmap of Distances of Data sorted by Cls. Clustering algorithms provide a Classifcation of data, where the labels are defined as a numeric vector Cls. Then, a typical cluster-respectively group structure is displayed by the Heatmap function. At the margin of the heatmap a dendrogram can be shown, if hierarchical cluster algorithms are used [Wilkinson,2009]. Here the dendrogram has to be shown separately and only the heatmap itself is displayed

Usage

Heatmap(DataOrDistances,Cls,method='euclidean',

LowLim=0,HiLim,LineWidth=0.5,Clabel="Cluster No.")

Arguments

DataOrDistances

if not symmetric, then the function assumes a [1:n,1:d] numeric matrix of n data cases in rows amd d variables in columns. In this case, the distance metric specifed in method will be used.

Otherwise,

[1:n,1:n] distance matrix that is symmetric

Cls

[1:n] numerical vector of numbers defining the classification as the main output of the clustering algorithm. It has k unique numbers for k clusters that represent the arbitrary labels of the clustering, assuming a descending order of 1 to k. If not ordered please use ClusterRenameDescendingSize. Otherwise x and y label will be incorrect.

method

Optional, if DataOrDistances is a [1:n,1:d] not symmetric numerical matrix, please see parDist for accessible distance methods, default is Euclidean

LowLim

Optional: limits for the color axis

HiLim

Optional: limits for the color axis

LineWidth

Width of lines seperating the clusters in the heatmap

Clabel

Default "Cluster No.", for large number of clusters abbrevations can be used like "Cls No." or "C" in order to fit as the x and y axis labels

Details

"Cluster heatmaps are commonly used in biology and related fields to reveal hierarchical clusters in data matrices. Heatmaps visualize a data matrix by drawing a rectangular grid corresponding to rows and columns in the matrix and coloring the cells by their values in the data matrix. In their most basic form, heatmaps have been used for over a century [Wilkinson, 2012]. In addition to coloring cells, cluster heatmaps reorder the rows and/or columns of the matrix based on the results of hierarchical clustering. (...) . Cluster heatmaps have high data density, allowing them to compact large amounts of information into a small space [Weinstein, 2008]", [Engle, 2017].

The procedure can be adapted to distance matrices [Thrun, 2018]. Then, the color scale is chosen such that pixels of low distances have blue and teal colors, pixels of middle distances yellow colors, and pixels of high distances have orange and red colors [Thrun, 2018]. The distances are ordered by the clustering and the clusters are divided by black lines. A clustering is valid if the intra-cluster distances are distinctively smaller that inter-cluster distances in the heatmap [Thrun, 2018]. For another example, please see [Thrun, 2018] (Fig. 3.7, p. 31).

Value

object of ggplot2

Author(s)

Michael Thrun

References

[Wilkinson,2009] Wilkinson, L., & Friendly, M.: The history of the cluster heat map, The American Statistician, Vol. 63(2), pp. 179-184. 2009.

[Engle et al., 2017] Engle, S., Whalen, S., Joshi, A., & Pollard, K. S.: Unboxing cluster heatmaps, BMC bioinformatics, Vol. 18(2), pp. 63. 2017.

[Weinstein, 2008] Weinstein, J. N.: A postgenomic visual icon, Science, Vol. 319(5871), pp. 1772-1773. 2008.

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.

See Also

Pixelmatrix

Examples

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data

#Data
Heatmap(Data,Cls = Cls)

#Distances
Heatmap(as.matrix(dist(Data)),Cls = Cls)

Default color sequence for plots

Description

Defines the default color sequence for plots made with PixelMatrixPlot

Usage

data("HeatmapColors")

Format

A vector with different strings describing colors for this plot.


Inspect Boxplots

Description

Enables to inspect the boxplots for multiple variables in ggplot2 syntax. Each boxplot also has a point for the mean of the variable.

Usage

InspectBoxplots(Data, Names,Means=TRUE)

Arguments

Data

Matrix containing the data. Each column is one variable.

Names

Optional: Names of the variables. If missing the columnnames of data are used.

Means

Optional: TRUE: with mean, FALSE: Only median.

Value

The ggplot object of the boxplots

Author(s)

Felix Pape

Examples

x <- cbind(A = rnorm(200, 1, 3), B = rnorm(100, -2, 5))
InspectBoxplots(x)

Inspect the Correlation

Description

Inspects the correlation between two given features using density scatter plots.

Usage

InspectCorrelation(X, Y, DensityEstimation = "SDH",

CorMethod = "spearman", na.rm = TRUE,

SampleSize = round(sqrt(5e+08), -3),

NrOfContourLines = 20, Plotter = "native",

DrawTopView = T, xlab, ylab,

main = "Spearman correlation coef.:", xlim, ylim, 

Legendlab_ggplot = "value", ...)

Arguments

X

Numeric vector [1:n], first feature (for x axis values)

Y

Numeric vector [1:n], second feature (for y axis values)

DensityEstimation

"SDH" is very fast but maybe not correct, "PDE" is slow but proably more correct.

CorMethod

method of correlation of the cor function, One of "pearson" (default), "kendall", or "spearman

SampleSize

Numeric, positiv scalar, maximum size of the sample used for calculation. High values increase runtime significantly. The default is that no sample is drawn

na.rm

Function may not work with non finite values. If these cases should be automatically removed, set parameter TRUE

NrOfContourLines

Numeric, number of contour lines to be drawn. 20 by default.

Plotter

String, name of the plotting backend to use. Possible values are: "native", "ggplot", "plotly"

DrawTopView

Boolean, True means contur is drawn, otherwise a 3D plot is drawn. Default: TRUE

xlab

String, title of the x axis. Default: "X", see plot() function

ylab

String, title of the y axis. Default: "Y", see plot() function

main

string, the same as "main" in plot() function

xlim

see plot() function

ylim

see plot() function

Legendlab_ggplot

String, in case of Plotter="ggplot" label for the legend. Default: "value"

...

Density specifc parameters, for PDEscatter() or SDH (nbins,lambda,Xkernels,Ykernel))

Details

Example shows that features with high correlation coefficient do not correlate because of bimodality.

Value

plotting handler

Author(s)

Michael Thrun

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

See Also

DensityScatter

Examples

data(ITS)
data(MTY)
Inds=which(ITS<900&MTY<8000)

InspectCorrelation(ITS[Inds],MTY[Inds])

Inspection of Distance-Distribution

Description

Visualizes the distances between objects in the data matrix

Usage

InspectDistances(DataOrDistances,method= "euclidean",sampleSize = 50000,...)

Arguments

DataOrDistances

[1:n,1:d] data cases in rows, variables in columns, if not symmetric

or

[1:n,1:n] distance matrix, if symmetric

method

Optional, if Data[1:n,1:d] see parallelDist::parDist for distance method

sampleSize

double value defining the size of the sample for large distance matrizes, see InspectVariable

...

further arguments passed on to InspectVariable

Details

For an interpretation of the distribution analysis of the distance please read [Thrun, 2018, p. 27, 185].

Note

uses InspectVariable

Author(s)

Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20539-3, Heidelberg, 2018.

Examples

data("Lsun3D")
Data=Lsun3D$Data

InspectDistances(as.matrix(dist(Data)))

Pairwise scatterplots and optimal histograms

Description

Pairwise scatterplots and optimal histograms of all features stored as columns of data are plotted

Usage

InspectScatterplots(Data,Names=colnames(Data))

Arguments

Data

[1:n,1:d] Data cases in rows (n), variables in columns (d)

Names

Optional: Names of the variables. If missing the columnnames of data are used.

Details

For two features, PDEscatter function should be used to isnpect modalities [Thrun/Ultsch, 2018]. For many features the function takes too lang. In such a case this function can be used. See [Thrun/Ultsch, 2018] for optimal histogram description.

Author(s)

Michael Thrun

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A.: Effects of the payout system of income taxes to municipalities in Germany, 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, Vol. accepted, Foundation of the Cracow University of Economics, Zakopane, Poland, 2018.

Examples

Data=cbind(rnorm(100, mean = 2, sd = 3  ),rnorm(100,mean = 0, sd = 1),rnorm(100,mean = 6, sd = 0.5))
#InspectScatterplots(Data)

QQplot of Data versus Normalized Data

Description

Allows to inspect if standardization of data makes sense

Usage

InspectStandardization(Data, TransData, xug = -3, xog = 3, xlab = "Normal", yDataLab =

"Data", yTransDataLab = "Trasformated Data", Symbol4Gerade = "red", main = "", ...)

Arguments

Data

...

TransData

...

xug

...

xog

...

xlab

...

yDataLab

...

yTransDataLab

...

Symbol4Gerade

...

main

...

...

...

Details

...

Value

plot

Author(s)

Michael Thrun

References

Michael, J. R.: The stabilized probability plot, Biometrika, Vol. 70(1), pp. 11-17, 1983.


Visualization of Distribution of one variable

Description

Enables distribution inspection by visualization as described in [Thrun, 2018] and for example used in

Usage

InspectVariable(Feature, Name, i = 1, xlim, ylim,

 sampleSize =1e+05, main)

Arguments

Feature

[1:n] Variable/Vector of Data to be plotted

Name

Optional, string, for x label

i

Optional, No. of variable/feature, an integer of the for lope

xlim

[2] Optional, range of x-axis for PDEplot and histogram

ylim

[2] Optional, range of y-axis, only for PDEplot

sampleSize

Optional, default(100000), sample size, if datavector is to big

main

string for the title if other than what is desribed in N

Author(s)

Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20539-3, Heidelberg, 2018.

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

Examples

data("ITS")
InspectVariable(ITS,Name='Income in EUR',main='ITS')

Income Tax Share

Description

Numerical vector of length 11194. details in [Ultsch/Behnisch, 2017; Thrun/Ultsch, 2018].

Usage

data("ITS")

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch/Behnisch, 2017] Ultsch, A., Behnisch, M.: Effects of the payout system of income taxes to municipalities in Germany, Applied Geography, Vol. 81, pp. 21-31, 2017.

Examples

data(ITS)
str(ITS)

Jitters Unique Values

Description

Jitters Unique Values for Visualizations

Usage

JitterUniqueValues(Data, Npoints = 20,

min = 0.99999, max = 1.00001)

Arguments

Data

[1:n] vector of data

Npoints

number of jittered points generated from the m unique values of the datavector Data

min

minimum value of jittering

max

maximum value of jittering

Details

min and max are either multiplied or added to data depending on the range of values. If Npoints==2, then only two values per unique of Data is jittered otherwise additional values are generated.Npoints==1 does not jitter the values but gives the unique values back.

Value

vector of DataJitter[1:(m+Npoints-1)] jittered values

Author(s)

Michael Thrun

See Also

used for example in MDplot

Examples

data=c(rep(1,10),rep(0,10),rep(100,10))

JitterUniqueValues(data,Npoints=1)

JitterUniqueValues(data,Npoints=2)

DataJitter=JitterUniqueValues(data,Npoints=20)

Lsun3D inspired by FCPS [Thrun/Ultsch, 2020] introduced in [Thrun, 2018]

Description

Clearly defined clusters, different variances. Detailed description of dataset and its clustering challenge is provided in [Thrun/Ultsch, 2020].

Usage

data("Lsun3D")

Details

Size 404, Dimensions 3

Dataset defines discontinuites, where the clusters have different variances. Three main clusters, and four outliers (in cluster 4). For a more detailed description see [Thrun, 2018].

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.

[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Clustering Benchmark Datasets Exploiting the Fundamental Clustering Problems, Data in Brief, Vol. 30(C), pp. 105501, doi:10.1016/j.dib.2020.105501, 2020.

Examples

data(Lsun3D)
str(Lsun3D)
Cls=Lsun3D$Cls
Data=Lsun3D$Data

Minus versus Add plot

Description

Bland-Altman plot [Altman/Bland, 1983].

Usage

MAplot(X,Y,islog=TRUE,LoA=FALSE,CI=FALSE,

densityplot=FALSE,main,xlab,ylab,

Cls,lwd=2,ylim=NULL,...)

Arguments

X

[1:n] numerical vector of a feature/variable

Y

[1:n] another numerical vector of a feature/variable

islog

Optional, TRUE: MAplot, FALSE: M=x-y versus a=0.5(x+y)

LoA

Optional, if TRUE: limits of agreement are plottet as lines if densityplot=FALSE

CI

Optional, if TRUE: confidence intervals for LoA, see [Stockl et al., 2004], if densityplot=FALSE

densityplot

Optional, FALSE: Scatterplot using Classplot, TRUE: density scatter plot with DensityScatter

main

Optional, see plot

xlab

Optional, see plot

ylab

Optional, see plot

Cls

Optional, prior Classification as a numeric vector.

lwd

Optional, if LoA=TRUE or CI=TRUE the width of the lines, otherwise input argument is ignored

ylim

Optional, default =NULL sets this parameter automatically, otherwise see Classplot.

...

for example, ylim, Please see either Classplot in the mode Plotter="native", or DensityScatter for further arguments depending on densityplot, see also details

Details

Bland-Altman plot [Altman/Bland, 1983] for visual representation of genomic data or in order to decorrelate data.

"The limits of agreement (LoA) are defined as the mean difference +- 1.96 SD of differences. If these limits do not exceed the maximum allowed difference between methods (the differences within mean +- 1.96 SD are not clinically important), the two methods are considered to be in agreement and may be used interchangeably." cited as in URL. Please note, that the underyling assumption is the normal distribution of the differences. Input argument LoA=TRUE shows the mean of the difference in blue and +- 1.96 SD in green. Input argument CI=TRUE shows the mean of the difference in blue and the confidence intervall as red dashed lines similar to the cited URL.

In case of densityplot=FALSE, the function Classplot is always called with Plotter="native". Then, the input argument "Colors"" of points can only be set in Classplot if "Cls"" is given in this function, otherwise the points are always black. The input argument "Size"" sets the size of points in Classplot.

Value

MA

[1:n,2] Matrix of Minus component of two features and Add component of two features

Handle

see DensityScatter for output options, if densityplot=TRUE, otherwise NULL

Statistics

Named list of four element, each consisting of one value depending on input parameters LoA and CI, of this function. If not specifically set each list element is NULL. The elements are Mean_value - mean allowed difference, SD_value - standard deviation of difference, LoA_value - Limits of agreement=1.96*SD, CI_value - confidence intervall, i.e., maximum allowed difference

Author(s)

Michael Thrun

References

[Altman/Bland, 1983] Altman D.G., Bland J.M.: Measurement in medicine: the analysis of method comparison studies, The Statistician, Vol. 32, p. 307-317, doi:10.2307/2987937, 1983.

https://www.medcalc.org/manual/bland-altman-plot.php

[Stockl et al., 2004] Stockl, D., Rodriguez Cabaleiro, D., Van Uytfanghe, K., & Thienpont, L. M.: Interpreting method comparison studies by use of the Bland-Altman plot: reflecting the importance of sample size by incorporating confidence limits and predefined error limits in the graphic, Clinical chemistry, Vol. 50(11), pp. 2216-2218. 2004.

Examples

data("ITS")
data("MTY")
MAlist=MAplot(ITS,MTY)

Mirrored Density plot (MD-plot)

Description

This function creates a MD-plot for each variable of the data matrix. The MD-plot is a visualization for a boxplot-like shape of the PDF published in [Thrun et al., 2020] with the default ordering by shape. It is an improvement of violin or so-called bean plots and posses advantages in comparison to the conventional well-known box plot [Thrun et al., 2020].

A complete guide about the MDplot can be found in https://md-plot.readthedocs.io/en/latest/index.html.

Usage

MDplot(Data, Names, Ordering='Default', Scaling="None",

Fill='darkblue', RobustGaussian=TRUE, GaussianColor='magenta',

Gaussian_lwd=1.5, BoxPlot=FALSE,BoxColor='darkred', 

MDscaling='width', LineColor='black', LineSize=0.01,

QuantityThreshold=50, UniqueValuesThreshold=12,

SampleSize=5e+05,SizeOfJitteredPoints=1,OnlyPlotOutput=TRUE,

main="MD-plot",ylab="Range of values in which PDE is estimated",

BW=FALSE,ForceNames=FALSE)

Arguments

Data

[1:n,1:d] Numerical Matrix containing the n cases of d variables. Each column is one variable. A data.frame is automatically transformed to a numerical matrix.

Names

Optional: [1:d] Names of the variables. If missing, the columnnames of data are used. If not missing, than the names can be cleaned or not (see ForceNames).

Ordering

Optional: string, either Default, Columnwise or AsIs, Alphabetical, Average, Bimodal, Variance or Statistics. Please see details for explanation.

Scaling

Optional, Default is None, Percentalize, CompleteRobust, Robust or Log, Please see details for explanation.

Fill

Optional: String or Vector, which gives the color(s) with which MDs are to be filled with.

RobustGaussian

Optional: If TRUE: each MDplot of a variable is overlayed with a roubustly estimated unimodal Gaussian distribution in the range of this variable, if statistical testing does not yield a significant p.value. In this case the packages moments, diptest and signal are required.

GaussianColor

Optional: string, color of robustly estimated gaussian, only for RobustGaussian=TRUE.

Gaussian_lwd

Optional: numerical, line width of robustly estimated gaussian, only for RobustGaussian=TRUE.

BoxPlot

Optional: If TRUE: each MDplot is overlayed with a Box-Whisker Diagram.

BoxColor

Optional: string, color of Boxplot, only for BoxPlot=TRUE.

MDscaling

Optional: if "area", all violins have the same area (before trimming the tails). If "count", areas are scaled proportionally to the number of observations. If "width" (default), all MDs have the same maximum width.

LineColor

Optional: string, color of line around the mirrored densities. NA disables this features which is usefull if ones wants to avoid vertical lines leading to outliers.

LineSize

Optional: numerical, linewidth of line around the mirrored densities.

QuantityThreshold

Optional: numeric value defining the threshold of the minimal amount of values in data. Below this threshold no density estimation is performed and a 1D scatter plot with jittered points is drawn. Only Data Science experts should change this value after they understand how the density is estimated (see [Ultsch, 2005]).

UniqueValuesThreshold

Optional: numeric value defining the threshold of the minimal amount of unique values in data. Below this threshold no density estimation and statistical testing is performed and a 1D scatter plot with jittered points drawn. Only Data Science experts should change this value after they understand how the density is estimated (see [Ultsch, 2005]).

SampleSize

Optional: numeric value defining a threshold. Above this threshold uniform sampling of finite cases is performed in order to shorten computation time.If rowr is not installed, uniform sampling of all cases is performed. If required, SampleSize=n can be set to omit this procedure.

SizeOfJitteredPoints

Optional: scalar. If not enough unique values for density estimation are given, data points are jittered. This parameter defines the size of the points.

OnlyPlotOutput

Optional: Default TRUE only a ggplot object is given back, if FALSE: Additinally, scaled data and ordering are the output of this function in a list.

main

string defining the (centered) title of the plot

ylab

string defining the y label, PDE= pareto density estimation (see [Ultsch, 2005])

BW

FALSE: usual ggplot2 background and style which is good for screen visualizations

TRUE: theme_bw() is used which is more appropriate for publications

ForceNames

FALSE: Per Default column names are cleaned for propper plotting

TRUE: forces to set the column names as given. Beware, this can result in plotting errors.

Details

In short, the MD-plot can be described as a PDE optimized violin plot. The Pareto Density Estimation (PDE) is an approach to estimate the probability density function (pdf) [Ultsch, 2005].

The MD-plot is in the process of beeing peer-reviewed [Thrun/Ultsch, 2019].

Statistical testing is performed with dip.test and agostino.test.

For the paramter Ordering the following options are possible:

Default

Ordering of plots by convex/concav/unimodal/nonunimodal shapes using statistical criteria. In this case the signal is required.

Columnwise

Ordering of plots by the order of columns of Data.

AsIs

Synonym of Columnwise: Ordering of plots by the order of columns of Data.

Alphabetical

Ordering of plots by the order of columns of Data sorted in alphabetical order by column names.

Average

Ordering of plots by the order of columns of Data sorted in order of increasing column-wise average

Bimodal

Ordering of plots by the order of columns of Data sorted in order of decreasing bimodality amplitude[Zhang et al., 2003]

Variance

Ordering of plots by the order of columns of Data sorted in order of increasing inter-quartile range

Statistics

Ordering of plots depending on the logarithm of the p-vlaues of statistical testing. In this case the packages moments, diptest and signal are required.

For the paramter Scaling the following options are possible:

None

No Scaling of data is done.

Percentalize

Data is scaled between zero and 100.

CompleteRobust

Data is first robustly scaled between zero and 1, then centered to zero and outliers are capped by a robustly formula described in RobustNormalization.

Robust

Data is robustly scaled between zero and 1 by a formula described in the RobustNormalization.

Log

Data is transformed with a sgined log allowing for negative values to be transformed with a logarithm of base 10, please see SignedLog for details.

Value

In the default case of OnlyPlotOutput==TRUE: The ggplot object of the MD-plot.

Otherwise for OnlyPlotOutput==FALSE: A list of

ggplotObj

The ggplot object of the MD-plot.

Ordering

The ordering of columns of data defined by Ordering.

DataOrdered

[1:n,1:d] matrix of ordered and scaled data defined by Ordering and Scaling.

Note that the package ggExtra is not necessarily required but if given the feature names are automatically rotated.

Note

1.) One would assume that in the first of the two following cases ggplot2 only adjusts the plotting region but:

MDplot(MTY)+ylim(c(0,7000)) is equal to MDplot(MTY[MTY<7000]).

This means in both cases the data is clipped and AFTERWARDS the density estimation is performed.

2.) Because of a (sometimes) strange behavior of either ggplot2 or reshape2, numerical column names are changed to character by adding 'C_' which can disabled using ForceNames=TRUE.

3.) Columnnames will be automatically deblanked and cleaned. To force specific columnnames the input Names can be used in combination with ForceNames=TRUE. However, this can result in plotting errors or other strange behavior.

4.) Overlaying MD-plots with robustly estimated gaussians seldomly will yield magenta (or other GaussianColor) lines overlaying more than the violin plot they should overlay, because the width of the two plots is not the same (but I am unable to set it strictly in ggplot). In such a case just call the function again.

Author(s)

Michael Thrun, Felix Pape contributed with the idea to use ggplot2 as the basic framework.

References

[Thrun et al., 2020] Thrun, M. C., Gehlert, T. & Ultsch, A.: Analyzing the Fine Structure of Distributions, PLoS ONE, Vol. 15(10), pp. 1-66, DOI 10.1371/journal.pone.0238835, 2020.

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

[Zhang et al., 2003] Zhang, C., Mapes, B., & Soden, B.: Bimodality in tropical water vapour, Quarterly Journalof the Royal Meteorological Society, 129(594), 2847-2866, 2003.

See Also

https://md-plot.readthedocs.io/en/latest/index.html

ClassMDplot

https://pypi.org/project/md-plot/

Examples

x = cbind(
    A = runif(2000, 1, 5),
    B = c(rnorm(1000, 0, 1), rnorm(1000, 2.6, 1)),
    C = c(rnorm(2000, 2.5, 1)),
    D = rpois(2000, 5)
  )
MDplot(x)

Mirrored Density plot (MD-plot)for Multiple Vectors

Description

This function creates a MD-plot for multiple numerical vectors of various lenghts. The MD-plot is a visualization for a boxplot-like Shape of the PDF published in [Thrun et al., 2020]. It is an improvement of violin or so-called bean plots and posses advantages in comparison to the conventional well-known box plot [Thrun et al., 2020].

Usage

MDplot4multiplevectors(..., Names, Ordering = 'Columnwise',
Scaling = "None", Fill = 'darkblue', RobustGaussian = TRUE,

GaussianColor = 'magenta', Gaussian_lwd = 1.5, BoxPlot = FALSE,

BoxColor = 'darkred', MDscaling = 'width', LineSize = 0.01,

LineColor = 'black', QuantityThreshold = 40, UniqueValuesThreshold = 12,

SampleSize = 5e+05, SizeOfJitteredPoints = 1, OnlyPlotOutput = TRUE)

Arguments

...

Either d numerical vectors of different lengths or a list of length d where each element of the list is an vector of arbitrary length

Names

Optional: [1:d] Names of the variables. If missing, the columnnames of data are used.

Ordering

Optional: string, either Default, Columnwise, Alphabetical or Statistics. Please see details for explanation.

Scaling

Optional, Default is None, Percentalize, CompleteRobust, Robust or Log, Please see details for explanation.

Fill

Optional: string, color with which MDs are to be filled with.

RobustGaussian

Optional: If TRUE: each MDplot of a variable is overlayed with a roubustly estimated unimodal Gaussian distribution in the range of this variable, if statistical testing does not yield a significant p.value. In this case the packages moments, diptest and signal are required.

GaussianColor

Optional: string, color of robustly estimated gaussian, only for RobustGaussian=TRUE.

Gaussian_lwd

Optional: numerical, line width of robustly estimated gaussian, only for RobustGaussian=TRUE.

BoxPlot

Optional: If TRUE: each MDplot is overlayed with a Box-Whisker Diagram.

BoxColor

Optional: string, color of Boxplot, only for BoxPlot=TRUE.

MDscaling

Optional: if "area", all violins have the same area (before trimming the tails). If "count", areas are scaled proportionally to the number of observations. If "width" (default), all MDs have the same maximum width.

LineSize

Optional: numerical, linewidth of line around the mirrored densities.

LineColor

Optional: string, color of line around the mirrored densities. NA disables this features which is usefull if ones wants to avoid vertical lines leading to outliers.

QuantityThreshold

Optional: numeric value defining a threshold. Below this threshold no density estimation is performed and a jitter plot with a median line is drawn. Only Data Science experts should change this value after they understand how the density is estimated (see [Ultsch, 2005]).

UniqueValuesThreshold

Optional: numeric value defining a threshold. Below this threshold no density estimation and statistical testing is performed and a Jitter plot is drawn. Only Data Science experts should change this value after they understand how the density is estimated (see [Ultsch, 2005]).

SampleSize

Optional: numeric value defining a threshold. Above this threshold uniform sampling of finite cases is performed in order to shorten computation time.If rowr is not installed, uniform sampling of all cases is performed. If required, SampleSize=n can be set to omit this procedure.

SizeOfJitteredPoints

Optional: scalar. If Not enough unique values for density estimation are given, data points are jittered. This parameter defines the size of the points.

OnlyPlotOutput

Optional: Default TRUE only a ggplot object is given back, if FALSE: Additinally Scaled Data and ordering are the output of this function in a list.

Details

Please see MDplot for details.

Value

In the default case of OnlyPlotOutput==TRUE: The ggplot object of the MD-plot.

Otherwise for OnlyPlotOutput==FALSE: A list of

ggplotObj

The ggplot object of the MD-plot.

Ordering

The ordering of columns of data defined by Ordering.

DataOrdered

[1:n,1:d] matrix of ordered and scaled data defined by Ordering and Scaling.

Note that the package ggExtra is not necessarily required but if given the feauture names are automatically rotated.

Note

cbind.fill is internally used from the depricated R package rowr of Craig Varrichio.

Author(s)

Michael Thrun.

References

[Ultsch, 2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

[Thrun et al., 2020] Thrun, M. C., Gehlert, T. & Ultsch, A.: Analyzing the Fine Structure of Distributions, PLoS ONE, Vol. 15(10), pp. 1-66, DOI 10.1371/journal.pone.0238835, 2020.

See Also

ClassMDplot MDplot https://pypi.org/project/md-plot/

Examples

MDplot4multiplevectors(runif(20000, 1, 5),c(rnorm(20000,0,1),

rnorm(20000,2.6,1)),c(rnorm(2000,2.5,1)),rpois(25000,5),

Names=c('A','B','C','D'))

V=list(runif(20000, 1, 5),c(rnorm(20000,0,1),

rnorm(20000,2.6,1)),c(rnorm(2000,2.5,1)),rpois(25000,5))


MDplot4multiplevectors(V,Names=c('A','B','C','D'))

Robust Empirical Mean Estimation

Description

If the input is a matrix the mean value will be compute for every column.

Usage

Meanrobust(x, p=10,na.rm=TRUE)

Arguments

x

vetor or matrix

p

default=10; percent of the top- and bottomcut from x

na.rm

a boolean evaluating to TRUE or FALSE indicating whether all non finite values should be stripped before the computation proceeds.

Author(s)

Zornitsa Manolova

See Also

mean


Muncipal Income Tax Yield

Description

Numerical vector of length 11194. details in [Ultsch/Behnisch, 2017; Thrun/Ultsch, 2018].

Usage

data("MTY")

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Ultsch/Behnisch, 2017] Ultsch, A., Behnisch, M.: Effects of the payout system of income taxes to municipalities in Germany, Applied Geography, Vol. 81, pp. 21-31, 2017.

Examples

data(MTY)
str(MTY)

Plot multiple ggplots objects in one panel

Description

ggplot objects can be passed in ..., or to plotlist (as a list of ggplot objects)
For example, if the layout is specified as the matrix(c(1,2,3,3), nrow=2, byrow=TRUE), then plot 1 will go in the upper left, 2 will go in the upper right, and 3 will go all the way across the bottom.

Usage

Multiplot(..., Plotlist=NULL, ColNo=1, LayoutMat)

Arguments

...

multiple ggplot objects to be plotted

Plotlist

Optional: list filled with ggplot objects to be plotted

ColNo

Number of columns in layout

LayoutMat

A matrix specifying the layout. If present, 'ColNo' is ignored.

Value

List with Plotlist

Author(s)

Winston Chang

Examples

data(Lsun3D)
Data=Lsun3D$Data
Cls=Lsun3D$Cls
obj1=Classplot(Data[,1],Data[,2],Cls=Cls,Plotter="ggplot",Size=3,main="Top plot")
obj2=Classplot(Data[,2],Data[,3],Cls=Cls,Plotter="ggplot",Size=3,main="Middle plot")
obj3=Classplot(Data[,1],Data[,3],Cls=Cls,Plotter="ggplot",Size=3,main="Bottom plot")
V=Multiplot(obj1,obj2,obj3)

OpposingViolinBiclassPlot

Description

Creates a set of two violin plots opposing each other

Usage

OpposingViolinBiclassPlot(ListData, Names, BoxPlots = FALSE,
Subtitle = c("AttributeA", "AttributeB"),
Title = "Opposing Violin Biclass Plot")

Arguments

ListData

List of k matrices as elements where each element has shape [1:n, 1:2]

Names

Vector of character names for each element of ListData

BoxPlots

Optional: Boolean variable BoxPlots = TRUE shows a box plot drawn into the violin plot. BoxPlots = FALSE shows no box plot. Default: BoxPlots = FALSE

Subtitle

Optional: Vector of character names for two classes. The classes are described as features contained in the matrix [1:n, 1:2]

Title

Optional: Character containing the title of the plot.

Value

Plotly object.

Author(s)

Quirin Stier


Optimal Number Of Bins

Description

Optimal Number Of Bins is a kernel density estimation for fixed intervals.

Calculation of the optimal number of bins for a histogram.

Usage

OptimalNoBins(Data)

Arguments

Data

Data

Details

The bin width ist defined with bw=3.49*stdrobust(1/(n)^1/3)

Value

optNrOfBins The best possible number of bins. Not less than 10 though

Note

This the second version of the function prior available in AdaptGauss

Author(s)

Alfred Ultsch, Michael Thrun

References

David W. Scott Jerome P. Keating: A Primer on Density Estimation for the Great Home Run Race of 98, STATS 25, 1999, pp 16-22.

See Also

ParetoRadius

Examples

Data = c(rnorm(1000),rnorm(2000)+2,rnorm(1000)*2-1)

optNrOfBins = OptimalNoBins(Data)

minData = min(Data,na.rm = TRUE)

maxData = max(Data,na.rm = TRUE)

i = maxData-minData

optBreaks = seq(minData, maxData, i/optNrOfBins) # bins in fixed intervals 

hist(Data, breaks=optBreaks)

Pareto Density Estimation V3

Description

This function estimates the Pareto Density for the distribution of one variable. In the default setting the functions estimates internally the appropriate number and position of kernels to estimate the density properly. However, the user can set the kernels manually. In this case density will only be estimated only around these values even if data exists outside the range of kernels or the internally estimated paretoRadius does not contain all datapoints between each kernel. See example for details.

Usage

ParetoDensityEstimation(Data, paretoRadius, kernels = NULL,
  MinAnzKernels = 100,PlotIt=FALSE,Silent=FALSE)

Arguments

Data

[1:n] numeric vector of data.

paretoRadius

Optional scalar, numeric value, see ParetoRadius.If not given it is estimated internally. Please do not set manually

kernels

Optional,[1:m] numeric vector data values where pareto density is measured at. If 0 (by default) kernels will be computed.

MinAnzKernels

Optional, minimal number of kernels, default MinAnzKernels==100

PlotIt

Optional, if TRUE: raw basic r plot of density estimation of debugging purposes. Usually please use ggplot2 interface via PDEplot or MDplot

Silent

Optional, if TRUE: disables all warnings

Details

Pareto Density Estimation (PDE) is a method for the estimation of probability density functions using hyperspheres. The Pareto-radius of the hyperspheres is derived from the optimization of information for minimal set size. It is shown, that Pareto Density is the best estimate for clusters of Gaussian structure. The method is shown to be robust when cluster overlap and when the variances differ across clusters. This is the best density estimation to judge Gaussian Mixtures of the data see [Ultsch 2003].

If input argument kernels is set manually the output arguments paretoDensity_internal and kernels_internal provide the internally estimated density and kernels. Otherwise these arguments are NULL. The function provides a message if range of kernels and range of data does not overlap completly.

Typically it is not advisable to set paretoRadius manually. However in specific cases, the function ParetoRadius is used prior to calling this function. In such cases the input argument can use a priorly estimated paretoRadius.

Value

List With

kernels

[1:m] numeric vector. data values at with Pareto Density is measured.

paretoDensity

[1:m] numeric vector containing the determined density by paretoRadius.

paretoRadius

numeric value of defining the radius

kernels_internal

Either NULL or internally estimated [1:p] numeric vector of kernels if input argument kernels was set by the user

paretoDensity_internal

Either NULL or internally estimated density if input argument kernels was set by the user

Note

This the second version of the function prior available in AdaptGauss

Author(s)

Michael Thrun

References

Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

See Also

ParetoRadius

PDEplot

MDplot

Examples

#kernels are estimated internally
   data = c(rnorm(1000),rnorm(2000)+2,rnorm(1000)*2-1)
   pdeVal        <- ParetoDensityEstimation(data)
   plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
   yaxs='i',xlab='Data',ylab='PDE')
   
   ##data exist outside of the range kernels
   kernels=seq(from=-3,to=3,by=0.01) 
   pdeVal        <- ParetoDensityEstimation(data,  kernels=kernels)
   plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
   yaxs='i',xlab='Data',ylab='PDE')
   
   #data exists in-between kernels that is not measured
   pdeVal$paretoRadius#0.42
   kernels=seq(from=-8,to=8,by=1)
   pdeVal        <- ParetoDensityEstimation(data,  kernels=kernels)
   plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
   yaxs='i',xlab='Data',ylab='PDE')

ParetoRadius for distributions

Description

Calculation of the ParetoRadius i.e. the 18 percentiles of all mutual Euclidian distances in data.

Usage

ParetoRadius(Data, maximumNrSamples = 10000,
  plotDistancePercentiles = FALSE)

Arguments

Data

numeric data vector

maximumNrSamples

Optional, numeric. Maximum number for which the distance calculation can be done. 1000 by default.

plotDistancePercentiles

Optional, logical. If TRUE, a plot of the percentiles of distances is produced. FALSE by default.

Details

The Pareto-radius of the hyperspheres is derived from the optimization of information for minimal set size. ParetoRadius() is a kernel density estimation for variable intervals. It works only on Data without missing values (NA) or NaN. In other cases, please use ParetoDensityEstimation directly.

Value

numeric value, the Pareto radius.

Note

This the second version of the function prior available in AdaptGauss.

For larger datasets the quantile_c() function is used instead of quantile in R which was programmed by Dirk Eddelbuettel on Jun 6 and taken by the author from https://github.com/RcppCore/Rcpp/issues/967.

Author(s)

Michael Thrun

References

Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

See Also

ParetoDensityEstimation, OptimalNoBins


PDEnormrobust

Description

This functions plots ParetoDensityEsrtimation (PDE) and robustly estimated Gaussian with empirical Mean and Variance

Usage

PDEnormrobust(Data,xlab='PDE',ylab,main='PDEnormrobust',
                          PlotSymbolPDE='blue',
                          PlotSymbolGauss= 'magenta',PlotIt=TRUE,
                          Mark2Sigma=FALSE,Mark3Sigma=FALSE,
                          p_mean=10,p_sd=25,...)

Arguments

Data

numeric vector, data to be plotted.

xlab

Optional,see plot

ylab

Optional,see plot

main

Optional,see plot

PlotSymbolPDE

line color pdf

PlotSymbolGauss

line color robust gauss

Mark2Sigma

TRUE: sets to vertical lines marking data outside M+-1.96SD

Mark3Sigma

TRUE: sets to vertical lines marking data outside M+-2.576SD

p_mean

scalar between 1-99, percent of the top- and bottomcut from x

p_sd

scalar between 1-99, lowInnerPercentile for robustly estimated standard deviation

...

Further arguments for plot

Details

Within Mark2Sigma 95 percent of data should be contained if distribution is Gaussian

Within Mark3Sigma 99 percent of data should be contained if distribution is Gaussian

The 3sgima rule is usually defined as M+-3SD containing 99.7 percent of data but to simplify, the input parameter name is called Mark3Sigma instead Mark2comma576Sigma, the same reason applies to the output parameter Sigma3.

Value

Kernels

numeric vector. The x points of the PDE function.

ParetoDensity

estimated pdf of data, numeric vector, the PDE(x).

ParetoRadius

numeric value, the Pareto Radius used for the plot.

Normaldist

pdf based on rubstly estimated parameters

Pars

Named vector of robustly estimatated Mean, standard deviation SD, Sigma2=1.96*SD and Sigma3=2.576*SD, EstPercData_Sigma2, EstPercData_Sigma3

Author(s)

Michael Thrun

Examples

data(MTY)
PDEnormrobust(unname(MTY))

PDE plot

Description

This function plots the Pareto probability density estimation (PDE), uses PDEstimationForGauss and ParetoRadius.

Usage

PDEplot(Data, paretoRadius = 0, weight = 1, kernels = NULL,

                 LogPlot = F, PlotIt = TRUE, title =
                 "ParetoDensityEstimation(PDE)", color = "blue",
				 
                 xpoints = FALSE, xlim, ylim, xlab, ylab =
                 "PDE", ggPlot = ggplot(), sampleSize = 2e+05, lwd = 2)

Arguments

Data

[1:n] numeric vector of data to be plotted.

paretoRadius

numeric, the Pareto Radius. If omitted, calculate by paretoRad.

weight

numeric, Weight*ParetoDensity is plotted. 1 by default.

kernels

numeric vector of kernels. Optional

LogPlot

LogLog PDEplot if TRUE, xpoints has to be FALSE. Optional

PlotIt

logical, if plot. TRUE by default.

title

character vector, title of plot.

color

character vector, color of plot.

xpoints

logical, if TRUE only points are plotted. FALSE by default.

xlim

Arguments to be passed to the plot method.

ylim

Arguments to be passed to the plot method.

xlab

Arguments to be passed to the plot method.

ylab

Arguments to be passed to the plot method.

ggPlot

ggplot2 object to be plotted upon. Insert an exisiting plot to add a new PDEPlot to it. Default: empty plot

sampleSize

default(200000), sample size, if datavector is to big

lwd

linewidth, see plot

Value

kernels

numeric vector. The x points of the PDE function.

paretoDensity

numeric vector, the PDE(x).

paretoRadius

numeric value, the Pareto Radius used for the plot.

ggPlot

ggplot2 object. Can be used to further modify the plot or add other plots.

Author(s)

Michael Thrun

References

Ultsch, A.: Pareto Density Estimation: A Density Estimation for Knowledge Discovery, Baier D., Wernecke K.D. (Eds), In Innovations in Classification, Data Science, and Information Systems - Proceedings 27th Annual Conference of the German Classification Society (GfKL) 2003, Berlin, Heidelberg, Springer, pp, 91-100, 2005.

Examples

x <- rnorm(1000, mean = 0.5, sd = 0.5)
y <- rnorm(750, mean = -0.5, sd = 0.75)
plt <- PDEplot(x, color = "red")$ggPlot
plt <- PDEplot(y, color = "blue", ggPlot = plt)$ggPlot

# Second Example
#  ggplotObj=ggplot()
#  for(i in 1:length(Variables))
#     ggplotObj=PDEplot(Data[,i],ggPlot = ggplotObj)$ggPlot

The pie chart

Description

the pie chart represents amount of values given in data.

Usage

Piechart(Datavector,Names,Labels,MaxNumberOfSlices,
main='',col,Rline=1,...)

Arguments

Datavector

[1:n] a vector of n non unique values

Names

Optional, [1:k] names to search for in Datavector, if not set unique of Datavector is calculated.

Labels

Optional, [1:k] Labels if they are specially named, if not Names are used.

MaxNumberOfSlices

Default is k, integer value defining how many labels will be shown. Everything else will be summed up to Other.

main

Optional, title below the fan pie, see plot

col

Optional, the default are the first [1:k] colors of the default color sequence used in this package, otherwise a character vector of [1:k] specifying the colors analog to plot

Rline

Optional, the radius of the pie in numerical numbers

...

Optional, further arguments passed on to plot

Details

If Number of Slices is higher than MaxNumberOfSlices then ABCanalysis is applied (see [Ultsch/Lotsch, 2015]) and group A chosen. If Number of Slices in group A is higher than MaxNumberOfSlices, then the most important ones out of group A are chosen. If MaxNumberOfSlices is higher than Slices in group A, additional slices are shown depending on the percentage (from high to low). Parameters of visualization a set as in [Schwabish, 2014] defined.

Color sequence is automatically shortened to the MaxNumberOfSlices used in the pie chart.

Value

silent output by calling invisible of a list with

Percentages

[1:k] percent values visualized in fanplot

Labels

[1:k] see input Labels, only relevant ones

Note

You see in the example below that a pie chart does not visualize such data well contrary to the fanPlot.

Author(s)

Michael Thrun

References

[Schwabish, 2014] Schwabish, Jonathan A. An Economist's Guide to Visualizing Data. Journal of Economic Perspectives, 28 (1): 209-34. DOI: 10.1257/jep.28.1.209, 2014.

[Ultsch/Lotsch, 2015] Ultsch. A ., Lotsch J.: Computed ABC Analysis for Rational Selection of Most Informative Variables in Multivariate Data, PloS one, Vol. 10(6), pp. e0129767. doi 10.1371/journal.pone.0129767, 2015.

Examples

data(categoricalVariable)
Piechart(categoricalVariable)

Plot of a Pixel Matrix

Description

Plots Data matrix as a pixel coulour image.

Usage

Pixelmatrix(Data, XNames, LowLim, HiLim,

YNames, main,FillNotFiniteWithHighestValue=FALSE)

Arguments

Data

[1:n,1:d] Data cases in rows (n), variables in columns (d)

LowLim

Optional: limits for the color axis

HiLim

Optional: limits for the color axis

XNames

Optional: Vector - names for the X-ticks, NULL: no ticks at all

YNames

Optional: Vector - names for the Y-ticks, NULL: no ticks at all

main

Optoinal: String - Title of the plot

FillNotFiniteWithHighestValue

Optional: TRUE: fills not finite values with same color as the highest value

Details

Low values are shown in blue and green, middle values in yellow and high values in orange and red.

Author(s)

Michael Thrun, Felix Pape

Examples

data("Lsun3D")
Data=Lsun3D$Data

Pixelmatrix(Data)

3D plot of points

Description

A wrapper for Data with systematic clustering colors for either a 2D (x,y) or 3D (x,y,z) plot combined with a classification

Usage

Plot3D(Data,Cls,UniqueColors,

size=2,na.rm=FALSE,Plotter3D="rgl",...)

Arguments

Data

[1:n,1:d] matrix with either d=2 or d=3, if d>3 only the first 3 dimensions are taken

Cls

[1:n] numeric vector of the classification of data with k classes

UniqueColors

[1:k] character vector of colors, if not given DataVisualizations::DefaultColorSequence is used

size

size of points, for plotly additional a vector [1:n] of a mapping of sizes to Cls has to be given in the (...) argument with sizes=

na.rm

if na.rm=TRUE, then missing values are removed

Plotter3D

in case of 3 dimensions, choose either "plotly" or "rgl",

if one of this packages is not given, the other one is selected as a fallback method

...

further arguments to be processed by plot3d or geom_point or plot_ly of type "scatter3d"

Details

For geom_point only size and na.rm is available as further arguments.

Note

Uses either geom_point for 2D or plot3d for 3D or plot_ly

Author(s)

Michael Thrun

References

RGL vignette in https://cran.r-project.org/package=rgl

Examples

#Spin3D similar output

data(Lsun3D)
Plot3D(Lsun3D$Data,Lsun3D$Cls,type='s',radius=0.1,box=FALSE,aspect=TRUE)
rgl::grid3d(c("x", "y", "z"))


#Projected Points with Classification
Data=cbind(runif(500,min=-3,max=3),rnorm(500))

# Classification
Cls=ifelse(Data[,1]>0,1,2)
Plot3D(Data,Cls,UniqueColors = DataVisualizations::DefaultColorSequence[c(1,3)],size=2)

## Not run: 
#Points with Non-Overlapping Labels
#require(ggrepel)
Data=cbind(runif(30,min=-1,max=1),rnorm(30,0,0.5))
Names=paste0('VeryLongName',1:30)
ggobj=Plot3D(Data)
ggobj +  geom_text_repel(aes(label=Names), size=3)

## End(Not run)

PlotGraph2D

Description

plots a neighborhood graph in two dimensions given the 2D coordinates of the points

Usage

PlotGraph2D(AdjacencyMatrix, Points, Cls, Colors, xlab = "X", ylab = "Y", xlim,
ylim, Plotter = "native", LineColor = "grey", pch = 20, lwd = 0.1, main = "",
mainSize)

Arguments

AdjacencyMatrix

[1:n,1:n] numerical matrix consting of binary values. 1 indicates that two points have an edge, zero that they do not

Points

[1:n,1:2] numeric matrix of two feature

Cls

[1:n] numeric vector of k classes, if not set per default every point is in first class

Colors

Optional, string defining the k colors, one per class

xlab

Optional, string for xlabel

ylab

Optional, string for ylabel

xlim

Optional, [1:2] vector of x-axis limits

ylim

Optional, [1:2] vector of y-axis limits

Plotter

Optional, either "native" or "plotly"

LineColor

Optional, color of edges

pch

Optional, shape of point, usally can be in a range from zero to 25, see pch of plot for details

lwd

width of the lines

main

Optional, string for the title of plot

mainSize

Optional, scalar for the size of the title of plot

Details

The points are the vertices of the graph. the adjacency matrix defines the edges. Via adjacency matrix various graphs, like from deldir package, can be used.

Value

native plot or plotly object depending on input argument Plotter

Author(s)

Michael Thrun

References

Lecture of Knowledge Discovery II

See Also

pch

Examples

N=10
x=runif(N)
y=runif(N)
Euklid=as.matrix(dist(cbind(x,y)))
Radius=quantile(as.vector(Euklid),0.5)
RKugelGraphAdjMatrix = matrix(0, ncol = N, nrow = N)
for (i in 1:N) {
  RInd = which(Euklid[i, ] <= Radius, arr.ind = TRUE)
  RKugelGraphAdjMatrix[i, RInd] = 1
}
PlotGraph2D(RKugelGraphAdjMatrix,cbind(x,y))

Plot of the Amount Of Missing Values

Description

Percentage of missing values per feature are visualized as a bar plot.

Usage

PlotMissingvalues(Data,Names,

WhichDefineMissing=c('NA','NaN','DUMMY','.',' '),

PlotIt=TRUE,

xlab='Amount Of Missing Values in Percent',

xlim=c(0,100),...)

Arguments

Data

[1:n,1:d] data cases in rows, variables/features in columns

Names

[1:d] optional vector of string describing the names of the features

WhichDefineMissing

[1:d] optional vector of string describing missing values, usefull for character features. Currently up to five different options are possible.

PlotIt

If FALES: Does not plot

xlab

x label of bar plot

xlim

x axis limits in percent

...

Further arguments passed on to barplot, such as main for title

Value

plots not finite and missing values as a bar plot for each feature d and returns with invisible the amount of missing values as a vector. Works even with character variables, but WhichDefineMissing cannot be changed at the current version. Please make a suggestion on GitHub how to improve this.

Note

Does not work with the tibble format, in such a case please call as.data.frame(as.matrix(Data))

Author(s)

Michael Thrun

Examples

data("ITS")
data("MTY")

PlotMissingvalues(cbind(ITS,MTY),Names=c('ITS','MTY'))

Product-Ratio Plot

Description

The product-ratio plot as defined in [Tukey, 1977, p. 594].

Usage

PlotProductratio(X, Y, na.rm = FALSE, 

main='Product Ratio Analysis',xlab = "Log of Ratio",ylab = "Root of Product", ...)

Arguments

X

[1:n] positive numerical vector, negativ values are removed automatically

Y

[1:n] positive numerical vector, negativ values are removed automatically

na.rm

Function may not work with non finite values. If these cases should be automatically removed, set parameter TRUE

main

see plot

ylab

see plot

xlab

see plot

...

further arguments passed on to plot

Details

In the case where there are many instances of very small values, but a small number of very large ones, this plot is usefull [Tukey, 1977, p. 615].

Value

matrix[1:n,2] with sqrt(x*y) and log(x/y) as the two columns

Author(s)

Michael Thrun

References

[Tukey, 1977] Tukey, J. W.: Exploratory data analysis, United States Addison-Wesley Publishing Company, ISBN: 0-201-07616-0, 1977.

Examples

#Beware: The data does no fit ne requirements for this approach
data('ITS')
data(MTY)
PlotProductratio(ITS,MTY)

P-Matrix colors

Description

Defines the default color sequence for plots made with PDEscatter

Usage

data("PmatrixColormap")

Format

Returns the vectors for a (heat) colormap.


QQplot with a Linear Fit

Description

Qantile-quantile plot with a linear fit

Usage

QQplot(X,Y,Type=8,NoQuantiles=10000,xlab, ylab,col="red",main='',
lwd=3,pch=20,subplot=FALSE,...)

Arguments

X

[1:n] numerical vector, First Feature

Y

1:n] numerical vector, Second Feature to compare first feature with

Type

an integer between 1 and 9 selecting one of the nine quantile algorithms detailed in quantile

NoQuantiles

number of quantiles used in QQ-plot, if number is low and the data has outliers, there may be empty space visible in the plot

xlab

x label, see plot ...

ylab

y label, see plot

col

color of line, see plot

main

title of plot, see plot

lwd

line width of plot, see plot

pch

type of point, see plot

subplot

FALSE: par is set specifically, TRUE: assumption is the usage as a subfigure, par has to be set by the user, no checks are performed, labels have to be set by the user

...

other parameters for qqplot

Details

Output is the evaluation of a linear (regression) fit of lm called 'line' and a quantile quantile plot (QQplot). Per default 10.000 quantiles are chosen, but in the case of very large data vectors one can reduce the quantiles for faster computation. The 100 percentiles used for the regression line are of darker blue than the quantiles chosen by the user.

Value

List with

Quantiles

[1:NoQuantiles,1:2] quantiles in y and y

Residuals

Output of the Regression with residuals.lm(line)

Summary

Output of the Regression with summaryline)

Anova

Output of the Regression with anova(line)

Author(s)

Michael Thrun

References

Michael, J. R.: The stabilized probability plot, Biometrika, Vol. 70(1), pp. 11-17, 1983.

Examples

data(MTY)
NormalDistribution=rnorm(50000)
QQplot(NormalDistribution,MTY)

Transforms the Robust Normalization back

Description

Transforms the Robust Normalization back if Capped=FALSE

Usage

RobustNorm_BackTrafo(TransformedData,

MinX,Denom,Center=0)

Arguments

TransformedData

[1:n,1:d] matrix

MinX

scalar

Denom

scalar

Center

scalar

Details

For details see RobustNormalization

Value

[1:n,1:d] Data matrix

Author(s)

Michael Thrun

See Also

RobustNormalization

Examples

data(Lsun3D)
Data = Lsun3D$Data
TransList = RobustNormalization(Data, Centered = TRUE, WithBackTransformation = TRUE)

Lsun3DData = RobustNorm_BackTrafo(TransList$TransformedData,
                                 TransList$MinX,
                                 TransList$Denom,
                                 TransList$Center)

sum(Lsun3DData - Data) #<e-15

RobustNormalization

Description

RobustNormalization as described in [Milligan/Cooper, 1988].

Usage

RobustNormalization(Data,Centered=FALSE,Capped=FALSE,

na.rm=TRUE,WithBackTransformation=FALSE,

pmin=0.01,pmax=0.99)

Arguments

Data

[1:n,1:d] data matrix of n cases and d features

Centered

centered data around zero by median if TRUE

Capped

TRUE: outliers are capped above 1 or below -1 and set to 1 or -1.

na.rm

If TRUE, infinite vlaues are disregarded

WithBackTransformation

If in the case for forecasting with neural networks a backtransformation is required, this parameter can be set to 'TRUE'.

pmin

defines outliers on the lower end of scale

pmax

defines outliers on the higher end of scale

Details

Normalizes features either between -1 to 1 (Centered=TRUE) or 0-1 (Centered=TRUE) without changing the distribution of a feature itself. For a more precise description please read [Thrun, 2018, p.17].

"[The] scaling of the inputs determines the effective scaling of the weights in the last layer of a MLP with BP neural netowrk, it can have a large effect on the quality of the final solution. At the outset it is best to standardize all inputs to have mean zero and standard deviation 1 [(or at least the range under 1)]. This ensures all inputs are treated equally in the regularization prozess, and allows to choose a meaningful range for the random starting weights."[Friedman et al., 2012]

Value

if WithBackTransformation=FALSE: TransformedData[1:n,1:d] i.e., normalized data matrix of n cases and d features

if WithBackTransformation=TRUE: List with

TransformedData

[1:n,1:d] normalized data matrix of n cases and d features

MinX

[1:d] numerical vector used for manual back-transformation of each feature

MaxX

[1:d] numerical vector used for manual back-transformation of each feature

Denom

[1:d] numerical vector used for manual back-transformation of each feature

Center

[1:d] numerical vector used for manual back-transformation of each feature

Author(s)

Michael Thrun

References

[Milligan/Cooper, 1988] Milligan, G. W., & Cooper, M. C.: A study of standardization of variables in cluster analysis, Journal of Classification, Vol. 5(2), pp. 181-204. 1988.

[Friedman et al., 2012] Friedman, J., Hastie, T., & Tibshirani, R.: The Elements of Statistical Learning, (Second ed. Vol. 1), Springer series in statistics New York, NY, USA:, ISBN, 2012.

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, Heidelberg, ISBN: 978-3-658-20539-3, doi:10.1007/978-3-658-20540-9, 2018.

See Also

RobustNorm_BackTrafo

Examples

Scaled = RobustNormalization(rnorm(1000, 2, 100), Capped = TRUE)
hist(Scaled)

m = cbind(c(1, 2, 3), c(2, 6, 4))
List = RobustNormalization(m, FALSE, FALSE, FALSE, TRUE)
TransformedData = List$TransformedData

mback = RobustNorm_BackTrafo(TransformedData, List$MinX, List$Denom, List$Center)

sum(m - mback)

ROC plot

Description

ROC

Usage

ROC(Data, Cls, Names, Colors)

Arguments

Data

[1:n, 1:d] numeric vector or matrix of scores to be evaluated with ROC.

Cls

[1:n] numeric vector with true classes.

Names

[1:d] character vector with names for scores.

Colors

[1:d] character vector with colores for scores.

Value

ROCit

List of ROCit results for each score column in Data.

Plot

Plotly object.

Author(s)

Quirin Stier

Examples

Data = runif(1000,0,1)
Cls  = sample(c(0,1), 1000, replace = TRUE)
ROC(Data, Cls)

Shepard PDE scatter

Description

Draws ein Shepard Diagram (scatterplot of distances) with an two-dimensional PDE density estimation .

Usage

ShepardDensityScatter(InputDists, OutputDists, Plotter= "native", Type = "DDCAL",
DensityEstimation="SDH", Marginals = FALSE, xlab='Input Distances',
ylab='Output Distances',main='ProjectionMethod', sampleSize=500000)

Arguments

InputDists

[1:n,1:n] with n cases of data in d variables/features: Matrix containing the distances of the inputspace.

OutputDists

[1:n,1:n] with n cases of data in d dimensionalites of the projection method variables/features: Matrix containing the distances of the outputspace.

Plotter

Optional, either "native" or "plotly"

Type

Optional, either "DDCAL" which creates a special hard color transition sensitive to density-based structures or "Standard" which creates a standard continuous color transition which is proven to be not very sensitive for complex density-based structures.

DensityEstimation

Optional, use either "SDH" or "PDE" for data density estimation.

Marginals

Optional, either TRUE (draw Marginals) or FALSE (do not draw Marginals)

xlab

Label of the x axis in the resulting Plot.

ylab

Label of the y axis in the resulting Plot.

main

Title of the Shepard diagram

sampleSize

Optional, default(500000), reduces a.ount of data for density estimation, if too many distances given

Details

Introduced and described in [Thrun, 2018, p. 63] with examples in [Thrun, 2018, p. 71-72]

Author(s)

Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20540-9, Heidelberg, 2018.

Examples

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data
InputDist=as.matrix(dist(Data))
res = stats::cmdscale(d = InputDist, k = 2, eig = TRUE, 
        add = FALSE, x.ret = FALSE)

ProjectedPoints = as.matrix(res$points)
ShepardDensityScatter(InputDist,as.matrix(dist(ProjectedPoints)),main = 'MDS')
ShepardDensityScatter(InputDist[1:100,1:100],

as.matrix(dist(ProjectedPoints))[1:100,1:100],main = 'MDS')

Draws a Shepard Diagram

Description

This function plots a Shepard diagram which is a scatter plot of InputDist and OutputDist

Usage

Sheparddiagram(InputDists, OutputDists, xlab = "Input Distances",

                 ylab= "Output Distances", fancy = F,

				 main = "ProjectionMethod", gPlot = ggplot())

Arguments

InputDists

[1:n,1:n] with n cases of data in d variables/features: Matrix containing the distances of the inputspace.

OutputDists

[1:n,1:n] with n cases of data in d dimensionalites of the projection method variables/features: Matrix containing the distances of the outputspace.

xlab

Label of the x axis in the resulting Plot.

ylab

Label of the y axis in the resulting Plot.

fancy

Set FALSE for PC and TRUE for publication

main

Title of the Shepard diagram

gPlot

ggplot2 object to plot upon.

Value

ggplot2 object containing the plot.

Author(s)

Michael Thrun

Examples

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data
InputDist=as.matrix(dist(Data))
res = stats::cmdscale(d = InputDist, k = 2, eig = TRUE, 
        add = FALSE, x.ret = FALSE)
ProjectedPoints = as.matrix(res$points)


Sheparddiagram(InputDist,as.matrix(dist(ProjectedPoints)),main = 'MDS')

Signed Log

Description

Computes the Signed Log if Data

Usage

SignedLog(Data,Base="Ten")

Arguments

Data

[1:n,1:d] Data matrix with n cases and d variables

Base

Either "Ten", "Two", "Zero", or any number.

Details

A neat transformation for data, it it has a better representation on the log scale.

Value

Transformed Data

Note

Number Selections for Base for 2,10, "Two" or "Ten" add 1 to every datapoint as defined in the lectures.

Author(s)

Michael Thrun

References

Prof. Dr. habil. A. Ultsch, Lectures in Knowledge Discovery, 2014.

See Also

log

Examples

# sampling is done
# because otherwise the example takes too long
# in the CRAN check
data('ITS')
ind=sample(length(ITS),1000)

MDplot(SignedLog(cbind(ITS[ind],MTY[ind])*(-1),Base = "Ten"))

Silhouette plot of classified data.

Description

Silhouette plot of cluster silhouettes for the n-by-d data matrix Data or distance matrix where the clusters are defined in the vector Cls.

Usage

Silhouetteplot(DataOrDistances, Cls, method='euclidean',

PlotIt=TRUE,...)

Arguments

DataOrDistances

[1:n,1:d] data cases in rows, variables in columns, if not symmetric

or

[1:n,1:n] distance matrix, if symmetric

Cls

numeric vector, [1:n,1] classified data

method

Optional if Datamatrix is used, one of "euclidean", "maximum", "manhattan", "canberra", "binary" or "minkowski". Any unambiguous substring can be given, see dist

PlotIt

Optional, Default:TRUE, FALSE to supress the plot

...

If PlotIt=TRUE: Further arguements to barplot

Details

"The Silhouette plot is a common unsupervised index for visual evaluation of a clustering [L. R. Kaufman/Rousseeuw, 2005] [introduced in [Rousseeuw, 1987]]. A reasonable clustering is characterized by a silhouette width of greater than 0.5, and an average width below 0.2 should be interpreted as indicating a lack of any substantial cluster structure [Everitt et al., 2001, p. 105]. However, it is evident that silhouette scores assume clusters that are spherical or Gaussian in shape [Herrmann, 2011, pp. 91-92]" [Thrun, 2018, p. 29].

Value

silh

Silhouette values in a N-by-1 vector

Author(s)

Onno Hansen-Goos, Michael Thrun

References

[Thrun, 2018] Thrun, M. C.: Projection Based Clustering through Self-Organization and Swarm Intelligence, doctoral dissertation 2017, Springer, ISBN: 978-3-658-20539-3, Heidelberg, 2018.

[Rousseeuw, 1987] Rousseeuw, Peter J.: Silhouettes: a Graphical Aid to the Interpretation and Validation of Cluster Analysis, Computational and Applied Mathematics, 20, p.53-65, 1987.

Examples

data("Lsun3D")
Cls=Lsun3D$Cls
Data=Lsun3D$Data
#clear cluster structure
plot(Data[,1:2],col=Cls)
#However, the silhouette plot does not indicate a very good clustering in cluster 1 and 2
Silhouetteplot(Data,Cls = Cls,main='Silhouetteplot')

Slope Chart

Description

ABC analysis improved slope chart

Usage

Slopechart(FirstDatavector,

SecondDatavector,

Names,

Labels,

MaxNumberOfSlices,

TopLabels=c('FirstDatavector','SecondDatavector'),

main='Comparision of Descending Frequency')

Arguments

FirstDatavector

[1:n] a vector of n non unique values - a features

SecondDatavector

[1:m] a vector of n non unique values - a second feature

Labels

Optional, [1:k] Labels if they are specially named, if not Names are used.

Names

[1:k] names to search for in Datavector, if not set unique of Datavector is calculated.

MaxNumberOfSlices

Default is k, integer value defining how many labels will be shown. Everything else will be summed up to Other.

TopLabels

Labels of of feature names

main

title of the plot

Details

still experimental.

Value

silent output by calling invisible of a list with

Percentages

[1:k] percent values visualized in fanplot

Labels

[1:k] see input Labels, only relevant ones

Author(s)

Michael Thrun

References

[Gohil, 2015] Gohil, Atmajitsinh. R data Visualization cookbook. Packt Publishing Ltd, 2015.

See Also

Piechart, Fanplot

Examples

## will follow

Calculate Pareto density estimation for ggplot2 plots

Description

This function enables to replace the default density estimation for ggplot2 plots with the Pareto density estimation [Ultsch, 2005]. It is used for the PDE-Optimized violin plot published in [Thrun et al, 2018].

Usage

stat_pde_density(mapping = NULL,
                 data = NULL,
                 geom = "violin",
                 position = "dodge",
                 ...,
                 trim = TRUE,
                 scale = "area",
                 na.rm = FALSE,
                 show.legend = NA,
                 inherit.aes = TRUE)

Arguments

mapping

Set of aesthetic mappings created by aes() or aes_(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.

data

The data to be displayed in this layer. There are three options:

If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot().

A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created.

A function will be called with a single argument, the plot data. The return value must be a data.frame., and will be used as the layer data.

geom

The geometric object to use display the data

position

Position adjustment, either as a string, or the result of a call to a position adjustment function.

...

Other arguments passed on to layer(). These are often aesthetics, used to set an aesthetic to a fixed value, like color = "red" or size = 3. They may also be parameters to the paired geom/stat.

trim

This parameter only matters if you are displaying multiple densities in one plot. If 'FALSE', the default, each density is computed on the full range of the data. If 'TRUE', each density is computed over the range of that group: this typically means the estimated x values will not line-up, and hence you won't be able to stack density values.

scale

When used with geom_violin: if "area" (default), all violins have the same area (before trimming the tails). If "count", areas are scaled proportionally to the number of observations. If "width", all violins have the same maximum width.

na.rm

If FALSE (the default), removes missing values with a warning. If TRUE silently removes missing values.

show.legend

logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display.

inherit.aes

If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. borders().

Details

Pareto Density Estimation (PDE) is a method for the estimation of probability density functions using hyperspheres. The Pareto-radius of the hyperspheres is derived from the optimization of information for minimal set size. It is shown, that Pareto Density is the best estimate for clusters of Gaussian structure. The method is shown to be robust when cluster overlap and when the variances differ across clusters.

Author(s)

Felix Pape

References

Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

[Thrun et al, 2018] Thrun, M. C., Pape, F., & Ultsch, A. : Benchmarking Cluster Analysis Methods using PDE-Optimized Violin Plots, Proc. European Conference on Data Analysis (ECDA), accepted, Paderborn, Germany, 2018.

See Also

[ggplot2]stat_density

Examples

miris <- reshape2::melt(iris)

ggplot2::ggplot(miris, 

mapping = ggplot2::aes(y = .data$value, x = .data$variable)) +

ggplot2::geom_violin(stat = "PDEdensity")

Pareto Density Estimation

Description

Density Estimation for ggplot with a clear model behind it.

Format

The format is: Classes 'StatPDEdensity', 'Stat', 'ggproto' <ggproto object: Class StatPDEdensity, Stat> aesthetics: function compute_group: function compute_layer: function compute_panel: function default_aes: uneval extra_params: na.rm finish_layer: function non_missing_aes: parameters: function required_aes: x y retransform: TRUE setup_data: function setup_params: function super: <ggproto object: Class Stat>

Details

PDE was published in [Ultsch, 2005], short explanation in [Thrun, Ultsch 2018] and the PDE optimized violin plot was published in [Thrun et al., 2018].

References

[Ultsch,2005] Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

[Thrun, Ultsch 2018] Thrun, M. C., & Ultsch, A. : Effects of the payout system of income taxes to municipalities in Germany, in Papiez, M. & Smiech,, S. (eds.), Proc. 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 533-542, Cracow: Foundation of the Cracow University of Economics, Cracow, Poland, 2018.

[Thrun et al, 2018] Thrun, M. C., Pape, F., & Ultsch, A. : Benchmarking Cluster Analysis Methods using PDE-Optimized Violin Plots, Proc. European Conference on Data Analysis (ECDA), accepted, Paderborn, Germany, 2018.


Standard Deviation Robust

Description

Robust empirical estimation for standard deviation.NaNs are ignored.

Usage

Stdrobust(x, lowInnerPercentile=25,na.rm=TRUE)

Arguments

x

a numerical matrix

lowInnerPercentile

optional; default=25; standard deviation aproximated by percentilinterval.

na.rm

a boolean evaluating to TRUE or FALSE indicating whether all non finite values should be stripped before the computation proceeds.

Value

out

a vector with the calculated standard deviation for the column

Author(s)

Zornitsa Manolova

See Also

sd quantile


world_country_polygons

Description

world_country_polygons shapefile

Usage

data("world_country_polygons")

Format

world_country_polygons stores data objects using classes defined in the sp package or inheriting from those classes updated to sp Y= 1.4 and rgdal >= 1.5.

Since DataVisualization Version 1.2.1 it stores now a CRS objects with a comment containing an WKT2 CRS representation, thanks to a suggestion of Roger Bivand.

Details

Note that the rebuilt CRS object contains a revised version of the input Proj4 string as well as the WKT2 string, and may be used with both older and newer versions of sp. See maptools package for further details. Also note that since sp >= 2.0 maptools and rgdal were deprecated without change to the workflow. See terra for an alternative to maptools.

Author(s)

Hamza Tayyab, Michael Thrun

Source

maptools package

References

maptools package

Examples

data(world_country_polygons)
str(world_country_polygons)

plots a world map by country codes

Description

The Worldmap function is used in [Thrun, 2018].

Usage

Worldmap(CountryCodes, Cls, Colors, 

MissingCountryColor = grDevices::gray(0.8), ...)

Arguments

CountryCodes

[1:n] vector of characters identifying countries by ISO 3166 codes (2 or 3 letters)

Cls

[1:n] numerical vector of classification

Colors

optional, vector of charcters specifying the used colors

MissingCountryColor

if not all countries are specified in CountryCodes then the color of non relevant countries can be changed here

...

Further arguments passed on to plot, see also sp::SpatialPolygons-class

Value

List of

Colors

[1:m] colors used in map, m<=n

CountryCodeList

[1:m] countries found, m<=n

world_country_polygons

SpatialPolygonsDataFrame

Author(s)

Michae Thrun

References

Used in

[Thrun, 2018] Thrun, M. C. : Cluster Analysis of the World Gross-Domestic Product Based on Emergent Self-Organization of a Swarm, 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena, Foundation of the Cracow University of Economics, Zakopane, Poland, accepted, 2018.

Source for shapefile: - package maptoops and

Originally 'mappinghacks.com/data/TM_WORLD_BORDERS_SIMPL-0.2.zip', now available from https://github.com/nasa/World-Wind-Java/tree/master/WorldWind/testData/shapefiles

Examples

# data from [Thrun, 2018]
Cls=c(1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 
2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 
1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 
2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 3L, 2L, 2L, 2L, 1L, 
2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 
2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 
2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 
2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L
)
Codes=c("AFG", "AGO", "ALB", "ARG", "ATG", "AUS", "AUT", "BDI", "BEL", 
"BEN", "BFA", "BGD", "BGR", "BHR", "BHS", "BLZ", "BMU", "BOL", 
"BRA", "BRB", "BRN", "BTN", "BWA", "CAF", "CAN", "CH2", "CHE", 
"CHL", "CHN", "CIV", "CMR", "COG", "COL", "COM", "CPV", "CRI", 
"CUB", "CYP", "DJI", "DMA", "DNK", "DOM", "DZA", "ECU", "EGY", 
"ESP", "ETH", "FIN", "FJI", "FRA", "FSM", "GAB", "GBR", "GER", 
"GHA", "GIN", "GMB", "GNB", "GNQ", "GRC", "GRD", "GTM", "GUY", 
"HKG", "HND", "HTI", "HUN", "IDN", "IND", "IRL", "IRN", "IRQ", 
"ISL", "ISR", "ITA", "JAM", "JOR", "JPN", "KEN", "KHM", "KIR", 
"KNA", "KOR", "LAO", "LBN", "LBR", "LCA", "LKA", "LSO", "LUX", 
"MAC", "MAR", "MDG", "MDV", "MEX", "MHL", "MLI", "MLT", "MNG", 
"MOZ", "MRT", "MUS", "MWI", "MYS", "NAM", "NER", "NGA", "NIC", 
"NLD", "NOR", "NPL", "NZL", "OMN", "PAK", "PAN", "PER", "PHL", 
"PLW", "PNG", "POL", "PRI", "PRT", "PRY", "ROM", "RWA", "SDN", 
"SEN", "SGP", "SLB", "SLE", "SLV", "SOM", "STP", "SUR", "SWE", 
"SWZ", "SYC", "SYR", "TCD", "TGO", "THA", "TON", "TTO", "TUN", 
"TUR", "TWN", "TZA", "UGA", "URY", "USA", "VCT", "VEN", "VNM", 
"VUT", "WSM", "ZAF", "ZAR", "ZMB", "ZWE")
Worldmap(Codes,Cls)

Plotting for 3 dimensional data

Description

Plots z above xy plane as 3D mountain or 2D contourlines

Usage

zplot(x, y, z, DrawTopView = TRUE, NrOfContourLines = 20,

                 TwoDplotter = "native", xlim, ylim)

Arguments

x

Vector of x-coordinates of the data. If y and z are missing: Matrix containing 3 rows, one for each coordinate

y

Vector of y-coordinates of the data.

z

Vector of z-coordinates of the data.

DrawTopView

Optional: Boolean, if true plot contours otherwise a 3D plot. Default: True

NrOfContourLines

Optional: Numeric. Only used when DrawTopView == True. Number of lines to be drawn in 2D contour plots. Default: 20

TwoDplotter

Optional: String indicating which backend to use for plotting. Possible Values: 'ggplot', 'native', 'plotly'

xlim

[1:2] scalar vector setting the limits of x-axis

ylim

[1:2] scalar vector setting the limits of y-axis

Value

If the plotting backend does support it, this will return a handle for the generated plot.

Author(s)

Felix pape

Examples