DelaunayClassificationError: Delaunay Classification Error (DCE)

In Mthrun/DatabionicSwarm: Swarm Intelligence for Self-Organized Clustering

Delaunay Classification Error (DCE)

Description

DCE searches for the k-nearest neighbors of the first delaunay neighbors weighted by the Euclidean Distances of the Inputspace. DCE evaluates these neighbors in the Output space. A low value indicates a better two-dimensional projection of the high-dimensional Input space.

Usage

DelaunayClassificationError(Data,ProjectedPoints,Cls,LC,Gabriel=FALSE,
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
Gabriel	Optional, Boolean: TRUE/FALSE => Gabriel/Delauny graph (Default: FALSE => Delaunay)
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

Delaunay classification error (DCE) makes an unbiased evaluation of distance and densitiybased structure which ma be even non-linear seperable. First, DCE utilizes the information provided by a prior classification to assess projected structures. Second, DCE applies the insights drawn from graph theory. Details are described in [Thrun/Ultsch, 2018]

Value

list of

DCE	DelaunayClassificationError NOTE the rest is just for development purposes
DCEperPoint	[1:n] unnormalized DCE of each point: DCE = mean(DCEperPoint)
nn	the number of points in a relevant neghborhood: 0.5 * 85percentile(AnzNN)
AnzNN	[1:n] the number of points with a delaunay 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: DCEperPoint = HD*NNdists

Note

see also chapter 6 of [Thrun, 2018]

Author(s)

Michael Thrun

References

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A. : Investigating Quality measurements of projections for the Evaluation of Distance and Density-based Structures of High-Dimensional Data, Proc. European Conference on Data Analysis (ECDA), pp. accepted, Paderborn, Germany, 2018.

Examples

data(Hepta)

InputDistances=as.matrix(dist(Hepta$Data))
projection=Pswarm(InputDistances)
DelaunayClassificationError(Hepta$Data,projection$ProjectedPoints,Hepta$Cls,LC=projection$LC)$DCE

Mthrun/DatabionicSwarm documentation built on Nov. 2, 2023, 6:51 a.m.