Type:	Package
Title:	Credible Visualization for Two-Dimensional Projections of Data
Version:	0.1.8
Date:	2025-11-04
Maintainer:	Quirin Stier <Quirin_Stier@gmx.de>
Description:	Projections are common dimensionality reduction methods, which represent high-dimensional data in a two-dimensional space. However, when restricting the output space to two dimensions, which results in a two dimensional scatter plot (projection) of the data, low dimensional similarities do not represent high dimensional distances coercively [Thrun, 2018] <doi:10.1007/978-3-658-20540-9>. This could lead to a misleading interpretation of the underlying structures [Thrun, 2018]. By means of the 3D topographic map the generalized Umatrix is able to depict errors of these two-dimensional scatter plots. The package is derived from the book of Thrun, M.C.: "Projection Based Clustering through Self-Organization and Swarm Intelligence" (2018) <doi:10.1007/978-3-658-20540-9> and the main algorithm called simplified self-organizing map for dimensionality reduction methods is published in Thrun, M.C. and Ultsch, A.: "Uncovering High-dimensional Structures of Projections from Dimensionality Reduction Methods" (2020) <doi:10.1016/j.mex.2020.101093>.
License:	GPL-3
Imports:	Rcpp (≥ 1.0.8), RcppParallel (≥ 5.1.4), ggplot2, GeneralizedUmatrix
Suggests:	DataVisualizations, rgl, grid, mgcv, png, reshape2, fields, ABCanalysis, plotly, deldir, methods, knitr (≥ 1.12), rmarkdown (≥ 0.9), ProjectionBasedClustering
LinkingTo:	Rcpp, RcppArmadillo, RcppParallel
Depends:	R (≥ 3.0)
NeedsCompilation:	yes
SystemRequirements:	GNU make, pandoc (>=1.12.3, needed for vignettes), OpenCL shared library (provided by an SDK such as AMD/NVIDIA)
LazyLoad:	yes
LazyData:	TRUE
Encoding:	UTF-8
Packaged:	2025-11-12 11:01:36 UTC; quiri
Author:	Quirin Stier [aut, cre], Michael Thrun [aut, cph], The Khronos Group Inc. [cph]
Repository:	CRAN
Date/Publication:	2025-11-17 20:50:02 UTC

Credible Visualization for Two-Dimensional Projections of Data

Description

Projections are common dimensionality reduction methods, which represent high-dimensional data in a two-dimensional space. However, when restricting the output space to two dimensions, which results in a two dimensional scatter plot (projection) of the data, low dimensional similarities do not represent high dimensional distances coercively [Thrun, 2018] <DOI: 10.1007/978-3-658-20540-9>. This could lead to a misleading interpretation of the underlying structures [Thrun, 2018]. By means of the 3D topographic map the generalized Umatrix is able to depict errors of these two-dimensional scatter plots. The package is derived from the book of Thrun, M.C.: "Projection Based Clustering through Self-Organization and Swarm Intelligence" (2018) <DOI:10.1007/978-3-658-20540-9> and the main algorithm called simplified self-organizing map for dimensionality reduction methods is published in Thrun, M.C. and Ultsch, A.: "Uncovering High-dimensional Structures of Projections from Dimensionality Reduction Methods" (2020) <DOI:10.1016/j.mex.2020.101093>.

Details

For a brief introduction to GeneralizedUmatrixGPU please see the vignette Introduction of the Generalized Umatrix Package.

For further details regarding the generalized Umatrix see [Thrun, 2018], chapter 4-5, or [Thrun/Ultsch, 2020].

If you want to verifiy your clustering result externally, you can use Heatmap or SilhouettePlot of the CRAN package DataVisualizations.

Index of help topics:

Chainlink               Chainlink is part of the Fundamental Clustering
                        Problem Suit (FCPS) [Thrun/Ultsch, 2020].
DefaultColorSequence    Default color sequence for plots
GeneralizedUmatrixGPU   Generalized U-Matrix on GPU for Projection
                        Methods published in [Thrun/Ultsch, 2020]
GeneralizedUmatrixGPU-package
                        Credible Visualization for Two-Dimensional
                        Projections of Data

Author(s)

Michal Thrun

Maintainer: Michael Thrun <mthrun@informatik.uni-marburg.de>

References

[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Uncovering High-Dimensional Structures of Projections from Dimensionality Reduction Methods, MethodsX, Vol. 7, pp. 101093, DOI doi:10.1016/j.mex.2020.101093, 2020.

[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.

[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.

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$points)
#see also ProjectionBasedClustering package for other common projection methods
#see DatabionicSwarm for projection method without parameters or objective function
# ProjectedPoints=DatabionicSwarm::Pswarm(Data)$ProjectedPoints

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

Chainlink is part of the Fundamental Clustering Problem Suit (FCPS) [Thrun/Ultsch, 2020].

Description

linear not separable dataset of two interwined chains.

Usage

data("Chainlink")

Details

Size 1000, Dimensions 3, stored in Chainlink$Data

Teo clusters, stored in Chainlink$Cls

Published in [Ultsch et al.,1994] in German and [Ultsch 1995] in English.

References

[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.

[Ultsch 1995] Ultsch, A.: Self organizing neural networks perform different from statistical k-means clustering, Proc. Society for Information and Classification (GFKL), Vol. 1995, Basel 8th-10th March, 1995.

[Ultsch et al.,1994] Ultsch, A., Guimaraes, G., Korus, D., & Li, H.: Knowledge extraction from artificial neural networks and applications, Parallele Datenverarbeitung mit dem Transputer, pp. 148-16Chainlink, Springer, 1994.

Examples

data(Chainlink)
str(Chainlink)

## Not run: 
require(DataVisualizations)
DataVisualizations::Plot3D(Chainlink$Data,Chainlink$Cls)

## End(Not run)

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.

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

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

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, 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 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)