ICA {ProjectionBasedClustering}

Independent Component Analysis (ICA)

Description

Independent Component Analysis:

Negentropie: difference of entropy to a corresponding normally-distributed random variable J(y)=|E(G(y)-E(G(v)))|^2

Usage

ICA(Data,OutputDimension=2,Contrastfunction="logcosh",

Alpha=1,Iterations=200,PlotIt=FALSE,Cls)

Arguments

Data

numerical matrix of n cases in rows, d variables in columns, matrix is not symmetric.

OutputDimension

Number of dimensions in the Outputspace, default=2

Contrastfunction

Maximierung der Negentropie ueber geeignete geeignete Kontrastfunktion Default: 'logcosh' G(u)=1/a*log cosh(a*u) 'exp': G(u)=-exp(u^2/2)

Alpha

onstant with 1<=alpha<=2 used in approximation to neg-entropy when fun == "logcosh"

Iterations

maximum number of iterations to perform.

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

ProjectedPoints

[1:n,OutputDimension], n by OutputDimension matrix containing coordinates of the Projectio

Mixing

[1:OutputDimension,1:d] Mischungsmatrix s.d gilt Data=MixingMatrix*ProjectedPoints

Unmixing

Entmischungsmatrix with Data*Unmixing=ProjectedPoints

PCMatrix

pre-whitening matrix that projects data onto the first n.comp principal components.

Note

A wrapper for fastICA

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

Author(s)

Michael Thrun

Examples

data('Hepta')
Data=Hepta$Data

Proj=ICA(Data)

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

## End(Not run)