sominit.pca.kernelmatrix: Initialise the prototypes of a kernel SOM with kernel PCA

In yasomi: Yet Another Self Organising Map Implementation

Description

Initialise the prototypes of a kernel Self-Organising Map with a kernel Principal Component Analysis. The prototypes are regulary positioned (according to the prior structure) in the hyperplane spanned in the kernel induced feature space by the two first principal components of the data mapped in this space. If the kernel matrix contains standard Euclidean inner products vector data, then this method is equivalent to sominit.pca.default.

Usage

## S3 method for class 'kernelmatrix'
sominit.pca(data, somgrid, ...)

Arguments

data	the data to which the SOM will be fitted, i.e., a object of class "kernelmatrix"
somgrid	a somgrid object
...	not used

Details

The method first conducts an eigen analysis of the doubly centred kernel matrix. It generates a regular grid in the two dimensional representation space spanned by the first two eigen vectors and returns the coordinates of the nodes of the grid as linear combinations of the original points.

Value

A list with the following components

prototype	a matrix containing appropriate initial prototypes
D.c	the doubly centered kernel matrix
D.eigen	the result of the eigen analysis of D.c
sdev	standard deviations on each principal axis in kernel space

Author(s)

Fabrice Rossi

See Also

sominit.random and somgrid

Examples

data(iris)

X <- scale(as.matrix(unique(iris[1:2])))

sg <- somgrid(xdim=7,ydim=7,topo="rect")

proto <- sominit.pca(as.kernelmatrix(tcrossprod(X)),sg)$prototypes

proto.mapped <- proto%*%X

plot(X,pch="+",col="red",xlim=range(X[,1],proto.mapped[,1]),
     ylim=range(X[,2],proto.mapped[,2]))

points(proto.mapped,pch=20)

yasomi documentation built on May 2, 2019, 5:59 p.m.