CCA: Curvilinear Component Analysis (CCA)

In Mthrun/ProjectionBasedClustering: Projection Based Clustering

Curvilinear Component Analysis (CCA)

Description

CCA Projects data vectors using Curvilinear Component Analysis [Demartines/Herault, 1995],[Demartines/Herault, 1997].

Unknown values (NaN's) in the data: projections of vectors with unknown components tend to drift towards the center of the projection distribution. Projections of totally unknown vectors are set to unknown (NaN).

Usage

CCA(DataOrDistances,Epochs,OutputDimension=2,method='euclidean',

alpha0 = 0.5, lambda0,PlotIt=FALSE,Cls)

Arguments

DataOrDistances	Numerical matrix defined as either 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))
Epochs	Number of eppochs (scalar), i.e, training length
OutputDimension	Number of dimensions in the Outputspace, default=2
method	method specified by distance string. One of: 'euclidean','cityblock=manhatten','cosine','chebychev','jaccard','minkowski','manhattan','binary'
alpha0	(scalar) initial step size, 0.5 by default
lambda0	(scalar) initial radius of influence, 3*max(std(D)) by default
PlotIt	Default: FALSE, If TRUE: Plots the projection as a 2d visualization. OutputDimension>2: only the first two dimensions will be shown
Cls	[1:n,1] Optional,: only relevant if PlotIt=TRUE. Numeric vector, given Classification in numbers: every element is the cluster number of a certain corresponding element of data.

Details

An short overview of different types of projection methods can be found in [Thrun, 2018, p.42, Fig. 4.1] (doi: 10.1007/978-3-658-20540-9).

Value

A n by OutputDimension matrix containing coordinates of the projected points.

Note

Only Transfered from matlab to R. Matlabversion: Contributed to SOM Toolbox 2.0, February 2nd, 2000 by Juha Vesanto https://www.cis.hut.fi/projects/somtoolbox/

You can use the standard ShepardScatterPlot or the better approach through the ShepardDensityPlot of the CRAN package DataVisualizations.

Author(s)

Florian Lerch

References

[Demartines/Herault, 1997] Demartines, P., & Herault, J.: Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets, IEEE Transactions on Neural Networks, Vol. 8(1), pp. 148-154. 1997.

[Demartines/Herault, 1995] Demartines, P., & Herault, J.: CCA:" Curvilinear component analysis", Proc. 15 Colloque sur le traitement du signal et des images, Vol. 199, GRETSI, Groupe d'Etudes du Traitement du Signal et des Images, France 18-21 September, 1995.

Examples

data('Hepta')
Data=Hepta$Data

Proj=CCA(Data,Epochs=20)

## Not run: 
PlotProjectedPoints(Proj$ProjectedPoints,Hepta$Cls)

## End(Not run)

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