Package 'DRquality'

Title: Quality Measurements for Dimensionality Reduction
Description: Several quality measurements for investigating the performance of dimensionality reduction methods are provided here. In addition a new quality measurement called Gabriel classification error is made accessible.
Authors: Quirin Stier [aut], Florian Lerch [ctb], Julian Märte [aut], Hermann Tafo [ctb], Laukert Schlichting [ctb], Michael Thrun [aut, cph, cre]
Maintainer: Michael Thrun <[email protected]>
License: GPL-3
Version: 0.2.1
Built: 2024-10-09 05:00:53 UTC
Source: https://github.com/mthrun/drquality

Help Index

Classification Error (rate)

Description

Compares projected points to a given prior classification using knn classifier.

Usage

ClassificationError(OutputDistances,Cls,k=5)

Arguments

OutputDistances

[1:n,1:n]

Cls

[1:n]

k

number of k nearest neighbors, in Venna 2010 set to 5 (here default)

Details

Projected points are evaluated by k-nearest neighbor classification accuracy (with k = 5), that is, each sample in the visualization is classified by majority vote of its k nearest neighbors in the visualization, and the classification is compared to the ground truth label. [Venna 2010].

Value

Error

Classification Error: 1-Accuracy[1]
Accuracy

Accuracy

KNNCls

[1:n]] cls of knn classifier

Note

Here, the Outputdistances of the Projected points are used.

Author(s)

Michael Thrun

References

Venna, J., Peltonen, J., Nybo, K., Aidos, H., and Kaski, S. Information retrieval perspective to nonlinear dimensionality reduction for data visualization. The Journal of Machine Learning Research, 11, 451-490. (2010)

Gracia, A., Gonzalez, S., Robles, V., and Menasalvas, E. A methodology to compare Dimensionality Reduction algorithms in terms of loss of quality. Information Sciences, 270, 1-27. (2014)

Examples

if(requireNamespace("FCPS")){
data(Hepta,package="FCPS")
projection=cmdscale(dist(Hepta$Data), k=2)
ClassificationError(as.matrix(dist(projection)),Hepta$Cls)
}

C-Measure subtypes

Description

Calculate the C-Measure subtypes of minimal path length and minimal wiring

Arguments

Data

[1:n,1:d] numerical matrix of points in input space.
Projection

[1:n,1:2] numerical matrix of points in output space.
k

Number of nearest neighbors, both measures set it always to k=1.

Value

[[1:2] Numerical vector of MinimalPathlength and MinimalWiring values.

Author(s)

Michael Thrun

Examples

if(requireNamespace("FCPS")){
data(Hepta,package="FCPS")
projection=cmdscale(dist(Hepta$Data), k=2)
Cmeasure(Hepta$Data,projection)
}

Gabriel Classification Error (GCE)

Description

GCE searches for the k-nearest neighbors of the first gabriel neighbors weighted by the Euclidean Distances of the Inputspace [Thrun et al, 2023]. GCE evaluates these neighbors in the Output space. A low value indicates a better two-dimensional projection of the high-dimensional Input space.

Usage

GabrielClassificationError(Data,ProjectedPoints,Cls,LC,
PlotIt=FALSE,Plotter = "native", Colors = NULL,LineColor= 'grey',
main = "Name of Projection", mainSize = 24,xlab = "X", ylab = "Y", xlim, ylim,
pch,lwd,Margin=list(t=50,r=0,l=0,b=0))

Arguments

Data

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

[1:n,1:2] Numeric matrix with 2D points in cartesian coordinates
Cls

[1:n] Numeric vector with class labels
LC

Optional, Numeric vector of two values determining grid size of the underlying projection
PlotIt

Optional, Boolean: TRUE/FALSE => Plot/Do not plot (Default: FALSE)
Plotter

Optional, Character with plot technique (native or plotly)
Colors

Optional, Character vector of class colors for points
LineColor

Optional, Character of line color used for edges of graph
main

Optional, Character plot title
mainSize

Optional, Numeric size of plot title
xlab

Optional, Character name of x ax
ylab

Optional, Character name of y ax
xlim

Optional, Numeric vector with two values defining x ax range
ylim

Optional, Numeric vector with two values defining y ax range
pch

Optional, Numeric of point size (graphic parameter)
lwd

Optional, Numeric of linewidth (graphic parameter)
Margin

Optional, Margin of plotly plot

Details

Gabriek classification error (GCE) makes an unbiased evaluation of distance and densitiybased structure which ma be even non-linear seperable. First, GCE utilizes the information provided by a prior classification to assess projected structures. Second, GCE applies the insights drawn from graph theory. Details are described in [Thrun et al, 2023]

Value

list of

GCE

GabrielClassificationError NOTE the rest is just for development purposes
GCEperPoint

[1:n] unnormalized GCE of each point: GCE = mean(GCEperPoint)
nn

the number of points in a relevant neghborhood: 0.5 * 85percentile(AnzNN)
AnzNN

[1:n] the number of points with a gabriel graph neighborhood
NNdists

[1:n,1:nn] the distances within the relevant neighborhood, 0 for inner cluster distances
HD

[1:nn] HD = HarmonicDecay(nn) i.e weight function for the NNdists: GCEperPoint = HD*NNdists
IsInterDistance

Distances to the nn closest neighbors

GabrielDists

Distance matrix implied by high dimensional distances and the underlying gabriel (Gabriel) graph

ProjectionGraphError

Plotly object in case, plotly is chose

Author(s)

Michael Thrun, Quirin Stier, Julian Märte

References

[Thrun et al, 2023] Thrun, M.C, Märte, J., Stier, Q.: Analyzing Quality Measurements for Dimensionality Reduction, Machine Learning and Knowledge Extraction (MAKE), Vol 5., accepted, 2023.

Examples

if(requireNamespace("FCPS")){
data(Hepta,package="FCPS")
projection=cmdscale(dist(Hepta$Data), k=2)
GabrielClassificationError(Hepta$Data,projection,Hepta$Cls)$GCE
}


if(requireNamespace("FCPS")){
data(Hepta,package="FCPS")
projection=cmdscale(dist(Hepta$Data), k=2)
GabrielClassificationError(Hepta$Data,projection,Hepta$Cls)$GCE
}

Statistical correlation by Kendall

Description

Calculates the statistical correlation by Kendall. Basically a wrapper to pcaPP::cor.fk.

Usage

KendallsTau(InputDists, OutputDists)

Arguments

InputDists

Matrix containing the distances of the first dataset.

OutputDists

Matrix containing the distances of the second dataset.

Value

Equivalent to cor.fk

Author(s)

Michael Thrun

Examples

if(requireNamespace("FCPS")){
data(Hepta,package="FCPS")
InputDist=dist(Hepta$Data)
projection=cmdscale(InputDist, k=2)
KendallsTau(as.matrix(InputDist),as.matrix(dist(projection)))
}

Computes rank-based smoothed precision and recall

Description

Compares the projection in pData with the original data in Data and calculates trustworthiness and continuity of the projection for neighborhood sizes ranging from 1 to the size of the neighborhood.

Usage

plotMeasureRAAR(Raar, label = 'ProjectionMethod',
gPlotList = list(RAARplot = ggplot2::ggplot()), LineType="solid", Shape = 16,
PointsPerE = 10, fancy = FALSE)

Arguments

Raar

Output of RAAR() applied for a projection method.
label

Title of plot.
gPlotList

Settings for ggplot.
LineType

Character - graphic parameter: Line type of ggplot.
Shape

Integer: type of point
PointsPerE

Numeric graphic parameter: Distance between markers on plot line
fancy

Boolean graphic parameter: Some automatic settings for a more appealing plot.

Value

ggplot object

Author(s)

Michael Thrun

Computes rank-based smoothed precision and recall

Description

Compares the projection in pData with the original data in Data and calculates trustworthiness and continuity of the projection for neighborhood sizes ranging from 1 to the size of the neighborhood.

Usage

plotMeasureTundD(TDmatrix, label = 'ProjectionMethod',
gPlotList = list(TW = ggplot2::ggplot(), DC = ggplot2::ggplot()), LineType = "solid",
Shape = 16, PointsPerE = 16)

Arguments

TDmatrix

Output of MeasureTundD() applied for a projection method.
label

Title of plot.
gPlotList

Settings for ggplot.
LineType

Character - graphic parameter: Line type of ggplot.
Shape

Integer: type of point
PointsPerE

Numeric graphic parameter: Distance between markers on plot line

Value

ggplot object

Author(s)

Michael Thrun

Rescaled average agreement rate

Description

Rescaled average agreement rate deduced by the co-ranking matrix from LCMC.

Usage

RAAR(Data, ProjectedPoints, kmax = nrow(Data) - 2, PlotIt = T)

Arguments

Data

Matrix containing n cases in rows, d variables in columns or a distance matrix which in this case has to be symmetric

ProjectedPoints

n by OutputDimension matrix containing coordinates of the Projection

kmax

maximum of intervall 1:kmax of k nearest neighbors

PlotIt

Optional: Should the output be plottet. Default: TRUE

Value

A list containing:

Raar

Rescaled average agreement rate
Aar

Average agreement rate

Author(s)

Michael Thrun

References

Lee, J. A., Peluffo-Ordonez, D. H., & Verleysen, M. Multiscale stochastic neighbor embedding: Towards parameter-free dimensionality reduction. Paper presented at the Proceedings of 22st European Symposium on Artificial Neural Networks, Computational Intelligence And Machine Learning (ESANN) (2014).

Calculates the error of a projection with spearman's rank correlation coefficient

Description

Calculates the error of a projection with spearman's rank correlation coefficient.

Arguments

VectorOfInputDists(1:n2)

dissimilarities in Input Space between the n data points in vector form as produced by squareform(Dists(1:n,1:n))
VectorOfOutputDists(1:n2)

dissimilarities in Input Space between the n data points in vector form as produced by squareform(Dists(1:n,1:n))

Value

rho rank correlation coefficient

Author(s)

Florian Lerch

Calculates the error of a projection with spearman's rank correlation coefficient

Description

Calculates the error of a projection with spearman's rank correlation coefficient

Usage

SpearmansRho(InputDists, OutputDists)

Arguments

InputDists

[1:d,1:d] numeric matrix with input distances
OutputDists

[1:d,1:d] numeric matrix with output distances

Value

rho

Author(s)

Julian Märte

Topological Correlation

Description

Calculates the Topololgical Correlation

Usage

TopologicalCorrelation(Data,ProjectedPoints,type='norm',method,Kn=0)

Arguments

Data

a matrix of the given n-dim. points: the rows represent the points and the columns represent the coordinates in the n-dim. space.
ProjectedPoints

matrix of Projected Points, if missing, method should be set!
method

Determines whether the selected projections method for a given set of n-Dim. points is a good choice. Therefor, a result of 1 means the seleceted projections method is good, and a result value of 0 means that the Visualization of the given Data in the two dim. space doesnt fit for the problem.
type

How the paths in the adjacencematrix should be weighted, norm representes path lenthgs of 1 and eucldidean represents the distance in the euclidean metric.
Kn

k nearest neighbours in the graph. only needed in method is isomap and LocallyLinearEmbedding

Value

TC value

Author(s)

Hermann Tafo, Laukert Schlichting 07/2015

Examples

if(requireNamespace("FCPS")){
data(Hepta,package="FCPS")
projection=cmdscale(dist(Hepta$Data), k=2)
TopologicalCorrelation(Hepta$Data,projection)
}

A generalized version of the zrehen-measure which defines the neighbourhood by gabrielgraph and is therefore not restricted to grid-based projections.

Description

A generalized version of the zrehen-measure which defines the neighbourhood by gabrielgraph and is therefore not restricted to grid-based projections.

Arguments

Data

[1:n,1:d] points in input room with d attributes
Projection

[1:n,1:2] projected points in output room, with index,x,y or index,line,column
width

only necessary if toroid
height

only necessary if toroid
isToroid

are the points toroid?
isGrid

is the grid a toroid?
plotGabriel

plot the generated GabrielGraph

Value

List with

V$zrehen

the raw zrehen measure
V$normedzrehen

the zrehen measure normed by the number of neighbours
v$neighbourcounter

the number of possible neighbours by which the zrehen measure is normed

Author(s)

Florian Lerch 07/2015

Examples

if(requireNamespace("FCPS")){
data(Hepta,package="FCPS")
projection=cmdscale(dist(Hepta$Data), k=2)
ZrehenMeasure4All(Hepta$Data,projection)$zrehen
}