ProjectionPursuit {ProjectionBasedClustering}

Projection Pursuit

Description

In the absence of a generative model for the data the algorithm can be used to find the projection pursuit directions. Projection pursuit is a technique for finding 'interesting' directions in multidimensional datasets

Usage

ProjectionPursuit(Data,OutputDimension=2,Indexfunction="logcosh",

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

Arguments

Data

array of data: n cases in rows, d variables in columns, matrix is not symmetric or distance matrix, in this case matrix has to be symmetric

OutputDimension

Number of dimensions in the Outputspace, default=2

Indexfunction

Criterium for Minimization:

default: 'logcosh' G(u)=1/a*log cosh(a*u) (ICA) 'exp': G(u)=-exp(u^2/2) 'kernel' 1/(1* pi )*exp(r/2)

Alpha

constant 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

Note

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

Author(s)

Michael Thrun