KMeansSparseCluster {sparcl}

Performs sparse k-means clustering

Description

This function performs sparse k-means clustering. You must specify a number of clusters K and an L1 bound on w, the feature weights.

Usage

KMeansSparseCluster(x, K=NULL, wbounds = NULL, nstart = 20, silent =
FALSE, maxiter=6, centers=NULL)
## S3 method for class 'KMeansSparseCluster'
plot(x,...)
## S3 method for class 'KMeansSparseCluster'
print(x,...)

Arguments

x

An nxp data matrix. There are n observations and p features.

K

The number of clusters desired ("K" in K-means clustering). Must provide either K or centers.

wbounds

A single L1 bound on w (the feature weights), or a vector of L1 bounds on w. If wbound is small, then few features will have non-zero weights. If wbound is large then all features will have non-zero weights. Should be greater than 1.

nstart

The number of random starts for the k-means algorithm.

silent

Print out progress?

maxiter

The maximum number of iterations.

centers

Optional argument. If you want to run the k-means algorithm starting from a particular set of clusters, then you can enter the Kxp matrix of cluster centers here. Default use case involves taking centers=NULL and instead specifying K.

...

not used.

Details

We seek a p-vector of weights w (one per feature) and a set of clusters C1,...,CK that optimize

$maximize_C1,...,CK,w sum_j w_j BCSS_j$ subject to $||w||_2 <= 1, ||w||_1 <= wbound, w_j >= 0$

where $BCSS_j$ is the between cluster sum of squares for feature j. An iterative approach is taken: with w fixed, optimize with respect to C1,...,CK, and with C1,...,CK fixed, optimize with respect to w. Here, wbound is a tuning parameter which determines the L1 bound on w.

The non-zero elements of w indicate features that are used in the sparse clustering.

Value

If wbounds is a vector, then a list with elements as follows (one per element of wbounds). If wbounds is just a single value, then elements as follows:

ws

The p-vector of feature weights.

Cs

The clustering obtained.

Author(s)

Daniela M. Witten and Robert Tibshirani

References

Witten and Tibshirani (2009) A framework for feature selection in clustering.

See Also

KMeansSparseCluster.permute,HierarchicalSparseCluster

Examples

# generate data
set.seed(11)
x <- matrix(rnorm(50*70),ncol=70)
x[1:25,1:20] <- x[1:25,1:20]+1
x <- scale(x, TRUE, TRUE)
# choose tuning parameter
km.perm <- KMeansSparseCluster.permute(x,K=2,wbounds=seq(3,7,len=15),nperms=5)
print(km.perm)
plot(km.perm)
# run sparse k-means
km.out <- KMeansSparseCluster(x,K=2,wbounds=km.perm$bestw)
print(km.out)
plot(km.out)
# run sparse k-means for a range of tuning parameter values
km.out <- KMeansSparseCluster(x,K=2,wbounds=seq(1.3,4,len=8))
print(km.out)
plot(km.out)
# Run sparse k-means starting from a particular set of cluster centers
#in the k-means algorithm.
km.out <- KMeansSparseCluster(x,wbounds=2:7,centers=x[c(1,3,5),])