GeneralizedUmatrix-package {GeneralizedUmatrix}

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 <DOI: 10.1016/j.mex.2020.101093>.

Details

For a brief introduction to GeneralizedUmatrix 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:

CalcUstarmatrix         Calculate the U*matrix for a given Umatrix and
                        Pmatrix.
Chainlink               Chainlink is part of the Fundamental Clustering
                        Problem Suit (FCPS) [Thrun/Ultsch, 2020].
DefaultColorSequence    Default color sequence for plots
Delta3DWeightsC         intern function
EsomNeuronsAsList       Converts wts data (EsomNeurons) into the list
                        form
ExtendToroidalUmatrix   Extend Toroidal Umatrix
GeneralizedUmatrix      Generalized U-Matrix for Projection Methods
                        published in [Thrun/Ultsch, 2020]
GeneralizedUmatrix-package
                        Credible Visualization for Two-Dimensional
                        Projections of Data
GeneratePmatrix         Generates the P-matrix
ListAsEsomNeurons       Converts List to WTS
LowLand                 LowLand
NormalizeUmatrix        Normalize Umatrix
ReduceToLowLand         ReduceToLowLand
TopviewTopographicMap   Top view of the topographic map in 2D
Uheights4Data           Uheights4Data
UmatrixColormap         U-Matrix colors
UniqueBestMatchingUnits
                        UniqueBestMatchingUnits
XYcoords2LinesColumns   XYcoords2LinesColumns(X,Y) Converts points
                        given as x(i),y(i) coordinates to integer
                        coordinates Columns(i),Lines(i)
addRowWiseC             intern function
plotTopographicMap      Visualizes the generalized U-matrix in 3D
sESOM4BMUs              simplified ESOM
setdiffMatrix           setdiffMatrix shortens Matrix2Curt by those
                        rows that are in both matrices.
trainstepC              internal function for s-esom
upscaleUmatrix          Upscale a Umatrix grid

Author(s)

Michal Thrun

Maintainer: Michael Thrun <[e-mail]>

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

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

##Interactive Island Generation 
## from a tiled Umatrix (toroidal assumption)
## Not run: 
	Imx = ProjectionBasedClustering::interactiveGeneralizedUmatrixIsland(resUmatrix$Umatrix,
	resUmatrix$Bestmatches)
	plotTopographicMap(resUmatrix$Umatrix,

	resUmatrix$Bestmatches, Imx = Imx)

## End(Not run)
#External Verification
## Not run: 

 DataVisualizations::Heatmap(Data,Cls)
 #if spherical cluster strcuture
 DataVisualizations::SilhouettePlot(Data,Cls)

## End(Not run)