cba (version 0.2-25)

ccfkms: Clustering with Conjugate Convex Functions

Description

Partition a data set into convex sets using conjugate convex functions.

Usage

ccfkms(x, n, p = NULL, par = 2, max.iter = 100, opt.std = FALSE,
       opt.retry = 0, debug = FALSE)

Value

A list with the following components:

centers

a matrix of cluster means (final prototypes).

size

a vector of cluster sizes.

cl

a factor of cluster labels (indexes).

inv.inf

the inverted information of the partition.

par

see above.

opt.std

see above.

Arguments

x

a data matrix.

n

optional number of prototypes.

p

a matrix of initial prototypes.

par

type or parameter of conjugate convex function.

max.iter

maximum number of iterations.

opt.std

optionally standardize the data.

opt.retry

number of retries.

debug

optionally turn on debugging output.

Author

Christian Buchta

Details

Two types of conjugate convex functions are available: one that is based on powers of the norm of the prototype vectors and another that is based on a logarithmic transformation of the norm. Both are intended to obtain more robust partitions.

Using par = 2 is equivalent to performing ordinary k-means with Euclidean distances. par = 1 is equivalent to LVQ of Kohonen type (the directions of the prototypes from the center of the data are used), and par = 0 is equivalent to using 2*ln(cosh(|p|))/2.

Internally the algorithm uses sparse data structures and avoids computations with zero data values. Thus, the data must not be centered (the algorithm does this internally with the option to further standardize the data). For dense data this is slightly inefficient.

If initial prototypes are omitted the number of prototypes must be specified. In this case the initial prototypes are drawn from the data (without replacement).

If the number of retries is greater than zero the best among that number of trial solutions is returned. Note that the number of prototypes must be specified as the initial prototypes are sampled from the data.

The debugging output shows the iteration number, the inverted information and the variance of the current partition as a percentage of the total (if each data point were a cluster), and the number of active prototypes (those with at least one member, i.e. a data point that is not closer to any other prototype).

Note that the algorithm uses tie-breaking when it determines the cluster memberships of the samples.

References

Helmut Strasser and Klaus Poetzelberger. Data Compression by Unsupervised Classification. SFB Report Series, No. 10, 1997.

See Also

kmeans, cmeans, kkmeans for similar or related clustering techniques.

Examples

### extend proximus example
x <- rlbmat()
rownames(x) <- seq(dim(x)[1])
cm <- ccfkms(x, n=4, opt.retry=10)
pcm <- predict(cm, x)
if (FALSE) {
### using sparse data may be more time-efficient
### depending on the goodness of the implementation
### of subset, etc. in package Matrix.
require(Matrix)
#sx <- as(x, "dgRMatrix")    # currently broken
sx <- as(x, "dgCMatrix")
system.time(scm <- ccfkms(sx, n=4, opt.retry=50))
system.time(cm <- ccfkms(x, n=4, opt.retry=50))
}