ProjectionBasedClustering: Automatic Projection-based Clustering (PBC) [Thrun/Ultsch,...

In Mthrun/ProjectionBasedClustering: Projection Based Clustering

Automatic Projection-based Clustering (PBC) [Thrun/Ultsch, 2020]

Description

Three steps are necessary for PBC. First, a projection method has to be chosen to generate projected points of high-dimensional data points. Second, the generalized U*-matrix has to be applied to the projected points by using a simplified emergent self-organizing map (ESOM) algorithm which is an unsupervised neural network [Thrun, 2018]. The resulting generalized U-matrix can be visualized by the topographic map [Thrun et al., 2016]. Third, the clustering itself is built on top of the generalized U-matrix using the concept of the abstract U-Matrix and shortest graph paths using ShortestGraphPathsC.

Usage

ProjectionBasedClustering(k, DataOrDistances, BestMatches, LC,

StructureType = TRUE, PlotIt = FALSE, method = "euclidean")

Arguments

k	number of clusters, how many to you see in the 3d landscape?
DataOrDistances	Numerical matrix that will be used for clustering with one DataPoint per row, defined as either as Data, i.e., [1:n,1:d], nonsymmetric, and consists of n cases of d-dimensional data points with every case having d attributes, variables or features, or Distances, i.e.,[1:n,1:n], symmetric and consists of n cases, e.g., as.matrix(dist(Data,method))
BestMatches	[1:n,1:2] Matrix with positions of Bestmatches=ProjectedPoints, one matrix line per data point
LC	grid size c(Lines,Columns)
StructureType	Optional, bool; =TRUE: compact structure of clusters assumed, =FALSE: connected structure of clusters assumed. For the two options vor Clusters, see [Thrun, 2017] or Handl et al. 2006
PlotIt	Optional, bool, Plots Dendrogramm
method	Optional, distance method used in parallelDist if Data given.

Details

ProjectionBasedClustering is a flexible and robust clustering framework based on a chose projection method and projection method a parameter-free high-dimensional data visualization technique. The visualization combines projected points with a topographic map with hypsometric colors, defined by the generalized U-matrix (see package GeneralizedUmatrix function GeneralizedUmatrix).

The clustering method with no sensitive parameters is done in this function and the algorithm is introduced in detail in [Thrun/Ultsch, 2020]. The clustering can be verified by the visualization and vice versa. If you want to verifiy your clustering result externally, you can use Heatmap or SilhouettePlot of the CRAN package DataVisualizations.

If parallelDist is not installed, function automatically falls back to dist.

Value

Cls [1:n] vector with selected classes of the bestmatches. You can use plotTopographicMap(Umatrix,Bestmatches,Cls) for verification.

Note

Often it is better to mark the outliers manually after the prozess of clustering; use in this case the visualization plotTopographicMap of the package GeneralizedUmatrix. If you would like to mark the outliers interactivly in the visualization use the interactiveClustering function.

Author(s)

Michael Thrun

References

[Thrun et al., 2016] Thrun, M. C., Lerch, F., Lötsch, 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/Ultsch, 2017] Thrun, M.C., Ultsch, A.: Projection based Clustering, Conf. Int. Federation of Classification Societies (IFCS),DOI:10.13140/RG.2.2.13124.53124, Tokyo, 2017.

[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Using Projection based Clustering to Find Distance and Density based Clusters in High-Dimensional Data, Journal of Classification, Vol. in press, Springer, DOI: 10.1007/s00357-020-09373-2, 2020.

Examples

data('Hepta')
#Step I: 2d projection
projectionpoints=NeRV(Hepta$Data)

#Step II (Optional): Computation of Generalized Umatrix
library(GeneralizedUmatrix)
visualization=GeneralizedUmatrix(Data = Hepta$Data,projectionpoints)
# Visualizuation of GeneralizedUmatrix
library(GeneralizedUmatrix)
TopviewTopographicMap(visualization$Umatrix,visualization$Bestmatches)
#or in 3D if rgl package exists
#plotTopographicMap(visualization$Umatrix,visualization$Bestmatches)

# Step III: Automatic Clustering
trafo=Projection2Bestmatches(projectionpoints)
# number of Cluster from dendrogram  (PlotIt=T) or visualization above
Cls=ProjectionBasedClustering(k=7, Hepta$Data, 

trafo$Bestmatches, trafo$LC,PlotIt=TRUE)

# Verification of Clustering
TopviewTopographicMap(visualization$Umatrix,visualization$Bestmatches,Cls)
#or in 3D if rgl package exists
#plotTopographicMap(visualization$Umatrix,visualization$Bestmatches,Cls)

Mthrun/ProjectionBasedClustering documentation built on June 12, 2022, 1:12 p.m.