GabrielClassificationError {DRquality}

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

Gabriel Classification Error (GCE) makes an unbiased evaluation of distance- and density-based structures which might be even non-linear separable. 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 several entries containing first the GCE itself as main result followed by further entries which contain potential important information

GCE

Numeric: the 'Gabriel Classification Error'

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, 1 for inter cluster distances and 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 chosen.

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
}