GeneralizedUmatrixGPU: Generalized U-Matrix on GPU for Projection Methods published...

In GeneralizedUmatrixGPU: Credible Visualization for Two-Dimensional Projections of Data

Generalized U-Matrix on GPU for Projection Methods published in [Thrun/Ultsch, 2020]

Description

Generalized U-Matrix visualizes high-dimensional distance and density based structurs in two-dimensional scatter plots of projectios methods like CCA, MDS, PCA or NeRV [Ultsch/Thrun, 2017] with the help of a topographic map with hypsometrioc tints [Thrun et al. 2016] using a simplified emergent SOM published in [Thrun/Ultsch, 2020].

Usage

GeneralizedUmatrixGPU(Data, ProjectedPoints, PlotIt = FALSE, Cls = NULL,
Toroid = TRUE, Tiled = FALSE, DataPerEpoch = 1, Verbose = 0, ...)

Arguments

Data	[1:n,1:d] array of data: n cases in rows, d variables in columns.
ProjectedPoints	[1:n,2] matrix containing coordinates of the Projection: A matrix of the fitted configuration.
PlotIt	Optional,bool, defaut=FALSE, if =TRUE: U-Marix of every current Position of Databots will be shown.
Cls	Optional, For plotting, see plotUmatrix in package Umatrix.
Toroid	Optional, Default=TRUE, ==FALSE planar computation with borders defined by projection method ==TRUE: toroid borderless (toroidal) computation, the four borders defined by projection method are ignored.
Tiled	Optional,For plotting see plotUmatrix in package Umatrix
DataPerEpoch	Optional, scalar, value above zero and below 1 starts sampling and defines percentage of data points sampled in each epoch during the learning phase. Beware: Experimental!
Verbose	Integer, determining text output during computation (Verbose > 0) or silent mode (Verbose=0).
...	Further parameters.

Details

Introduced first in the PhD thesis in [Thrun, 2018, p.46]. Furthermore the two parts of the work were peer-reviewed and published in [Ultsch/Thrun, 2017, Thrun/Ultsch, 2020].

Value

List with

Umatrix	[1:Lines,1:Columns] Umatrix to be plotted, numerical matrix storing the U-heights, see [Thrun, 2018] for definition.
EsomNeurons	[1:Lines,1:Columns,1:weights] 3-dimensional numeric array (wide format), not wts (long format).
Bestmatches	[1:n,1:2] Positions of GridConverted Projected Points on the Umatrix to the predefined Grid by Lines and Columns, First Columns has the content of the Line No and second Column of the Column number.
sESOMparamaters	internals for debugging
Lines	Number of Lines
Columns	Number of Columns
gplotres	output of ggplot2

Note

With the update of 01.01.2024, version 1.3 a minor change is included that is not mentioned in the referenced papers: for large number of cases and small radii the learning rate decays to 0.1 instead of remaining constant (any other case).

Author(s)

Quirin Stier, Michael Thrun

References

[Thrun et al., 2016] Thrun, M. C., Lerch, F., Loetsch, J., & Ultsch, A.: Visualization and 3D Printing of Multivariate Data of Biomarkers, in Skala, V. (Ed.), International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG), Vol. 24, Plzen, http://wscg.zcu.cz/wscg2016/short/A43-full.pdf, 2016.

[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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-3-658-20540-9")}, 2018.

[Ultsch/Thrun, 2017] Ultsch, A., & Thrun, M. C.: Credible Visualizations for Planar Projections, in Cottrell, M. (Ed.), 12th International Workshop on Self-Organizing Maps and Learning Vector Quantization, Clustering and Data Visualization (WSOM), IEEE Xplore, France, 2017.

[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Uncovering High-Dimensional Structures of Projections from Dimensionality Reduction Methods, MethodsX, Vol. 7, pp. 101093, DOI \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.mex.2020.101093")}, 2020.

Examples

library(GeneralizedUmatrix)
data("Chainlink")
Data=Chainlink$Data
Cls=Chainlink$Cls
InputDistances=as.matrix(dist(Data))
res=cmdscale(d=InputDistances, k = 2, eig = TRUE, add = FALSE, x.ret = FALSE)
ProjectedPoints=as.matrix(res$points)

if(requireNamespace("ProjectionBasedClustering")){
Stress = ProjectionBasedClustering::KruskalStress(InputDistances,
as.matrix(dist(ProjectedPoints)))
}


resUmatrix=GeneralizedUmatrixGPU(Data[1:2,], ProjectedPoints[1:2,])
#plotTopographicMap(resUmatrix$Umatrix,resUmatrix$Bestmatches)
#testing takes longer than 5 secs


resUmatrix=GeneralizedUmatrixGPU(Data,ProjectedPoints)
#plotTopographicMap(resUmatrix$Umatrix,resUmatrix$Bestmatches,Cls)

GeneralizedUmatrixGPU documentation built on Nov. 18, 2025, 1:06 a.m.