batchkmeans.kenelmatrix: Kernel K-means Clustering
In yasomi: Yet Another Self Organising Map Implementation

Description Usage Arguments Details Value Author(s) See Also Examples

Performs K-means clustering via an implicit mapping to a kernel induced feature space.

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## S3 method for class 'kernelmatrix'
batchkmeans(data, ncenters, init = c("prototypes", "random", "cluster"),
prototypes, weights, max.iter, verbose = FALSE, keepdata = TRUE, ...)

`data`	the data to cluster represented by a kernel matrix (an object of class `"kernelmatrix"`, see `as.kernelmatrix`).
`ncenters`	the number of clusters
`init`	the initialisation method (see `batchkmeans` for details)
`prototypes`	Initial values for the prototypes. It contains linear coefficients that describe the prototypes as linear combination of the initial data points mapped in the kernel induced feature space. It has therefore one row for each prototype (`ncenters`) and has many columns as data points. If missing, initial prototypes are chosen via the method specified by the `init` parameter (see details)
`weights`	optional weights for the data points
`max.iter`	maximal number of iterations of the algorithm
`verbose`	switch for tracing the clustering process
`keepdata`	if `TRUE`, the original data are returned as part of the result object
`...`	not used

This method implements Kernel K-means: the kernel is used to define an implicit mapping of the original data into a kernel induced feature space where a standard K-means is applied. The mapping is not explicitely carried out.

An object of class "batchkmeans" and of class "kernelbatchkmeans", a list with components including

`prototypes`	a matrix containing the coordinates of the prototypes: each row of the matrix sums to one and contains the coefficients of a linear combination of the original observations in the kernel induced feature space
`classif`	a vector of integer indicating to which cluster each observation has been assigned
`errors`	a vector containing the evolution of the quantisation error during the fitting process
`data`	the original data if the function is called with `keepdata = TRUE`
`weights`	the weights of the data points if the function is called with `keepdata = TRUE` and if the `weights` is given

Fabrice Rossi

See batchsom.kernelmatrix for Self-Oganising Map which provides both clustering and visualisation.

## inspired by the kmeans example in the stats package
require(graphics)

## 2 dimensional dataset
X <- cbind(rnorm(200,mean=2,sd=0.35),rnorm(200,mean=-1,sd=0.35))
Y <- cbind(runif(200,min=-1.5,max=-0.75),runif(200,min=0,max=0.5))
Z <- cbind(rnorm(200,sd=0.15),rnorm(200,sd=0.5))
M <- matrix(c(sin(pi/4),cos(pi/4),-cos(pi/4),sin(pi/4)),ncol=2)
U <- rbind(X,Y,Z%*%M+c(rep(0.25,200),rep(-0.5,200)))
U <- scale(U)

K <- as.kernelmatrix(tcrossprod(U))

km <- batchkmeans(K,3)

plot(U,col=km$classif,cex=0.5)

## map back the prototypes to the original space
points(km$prototypes%*%U,col=1:3,pch=20,cex=2)