GeneralizedUmatrix {GeneralizedUmatrix}

Generalized U-Matrix 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

GeneralizedUmatrix(Data,ProjectedPoints,

PlotIt=FALSE,Cls=NULL,Toroid=TRUE, Tiled=FALSE,

ComputeInR=FALSE,Parallel=TRUE,DataPerEpoch=1,...)

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 However, the amount of details shown will be less than in plotTopographicMap.

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

ComputeInR

Optional, =T: Rcode, =F Cpp Code

Parallel

Optional, =TRUE: compute parallel Cpp Code, =FALSE do not compute parallel Cpp Code

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!

...

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

Author(s)

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

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)
## Not run: 
Stress = ProjectionBasedClustering::KruskalStress(InputDistances,

as.matrix(dist(ProjectedPoints)))

## End(Not run)


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