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>.
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
SilhouettePlot of the CRAN package
Index: This package was not yet installed at build time.
Maintainer: Michael Thrun <firstname.lastname@example.org>
[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Uncovering High-Dimensional Structures of Projections from Dimensionality Reduction Methods, MethodsX, Vol. in press, pp. 101093. 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.
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)
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