cec {CEC}  R Documentation 
CrossEntropy Clustering
Description
cec
performs CrossEntropy Clustering on a data matrix.
See Details
for an explanation of CrossEntropy Clustering.
Usage
cec(
x,
centers,
type = c("covariance", "fixedr", "spherical", "diagonal", "eigenvalues", "mean", "all"),
iter.max = 25,
nstart = 1,
param,
centers.init = c("kmeans++", "random"),
card.min = "5%",
keep.removed = FALSE,
interactive = FALSE,
threads = 1,
split = FALSE,
split.depth = 8,
split.tries = 5,
split.limit = 100,
split.initial.starts = 1,
readline = TRUE
)
Arguments
x 
A numeric matrix of data. Each row corresponds to a distinct
observation; each column corresponds to a distinct variable/dimension. It
must not contain 
centers 
Either a matrix of initial centers or the number of initial
centers ( If If 
type 
The type (or types) of clustering (density family). This can be either a single value or a vector of length equal to the number of centers. Possible values are: "covariance", "fixedr", "spherical", "diagonal", "eigenvalues", "all" (default). Currently, if the 
iter.max 
The maximum number of iterations of the clustering algorithm. 
nstart 
The number of clusterings to perform (with different initial
centers). Only the best clustering (with the lowest cost) will be returned.
A value grater than 1 is valid only if the If the If the split mode is on ( 
param 
The parameter (or parameters) specific to a particular type of clustering. Not all types of clustering require parameters. The types that require parameter are: "covariance" (matrix parameter), "fixedr" (numeric parameter), "eigenvalues" (vector parameter). This can be a vector or a list (when one of the parameters is a matrix or a vector). 
centers.init 
The method used to automatically initialize the centers. Possible values are: "kmeans++" (default) and "random". 
card.min 
The minimal cluster cardinality. If the number of observations in a cluster becomes lower than card.min, the cluster is removed. This argument can be either an integer number or a string ending with a percent sign (e.g. "5%"). 
keep.removed 
If this parameter is TRUE, the removed clusters will be visible in the results as NA in the "centers" matrix (as well as the corresponding values in the list of covariances). 
interactive 
If 
threads 
The number of threads to use or "auto" to use the default
number of threads (usually the number of available processing units/cores)
when performing multiple starts ( The execution of a single start is always performed by a single thread, thus
for 
split 
If For each start ( 
split.depth 
The cluster subdivision depth used in split mode. Usually,
a value lower than 10 is sufficient (when after each splitting, new clusters
have similar sizes). For some data, splitting may often produce clusters
that will not be split further, in that case a higher value of

split.tries 
The number of attempts that are made when trying to split a cluster in split mode. 
split.limit 
The maximum number of centers to be discovered in split mode. 
split.initial.starts 
The number of 'standard' starts performed before starting the splitting process. 
readline 
Used only in the interactive mode. If 
Details
CrossEntropy Clustering (CEC) aims to partition m points into k clusters so as to minimize the cost function (energy E of the clustering) by switching the points between clusters. The presented method is based on the Hartigan approach, where we remove clusters which cardinalities decreased below some small prefixed level.
The energy function E is given by:
E(Y_1,\mathcal{F}_1;...;Y_k,\mathcal{F}_k) = \sum\limits_{i=1}^{k}
p(Y_i) \cdot (ln(p(Y_i)) + H^{\times}(Y_i\\mathcal{F}_i))
where Yi denotes the ith cluster, p(Yi) is the ratio of the number of points in ith cluster to the total number points, H(YiFi) is the value of crossentropy, which represents the internal cluster energy function of data Yi defined with respect to a certain Gaussian density family Fi, which encodes the type of clustering we consider.
The value of the internal energy function H depends on the covariance matrix (computed using maximumlikelihood) and the mean (in case of the mean model) of the points in the cluster. Seven implementations of H have been proposed (expressed as a type  model  of the clustering):
 "all":
All Gaussian densities. Data will form ellipsoids with arbitrary radiuses.
 "covariance":
Gaussian densities with a fixed given covariance. The shapes of clusters depend on the given covariance matrix (additional parameter).
 "fixedr":
Special case of 'covariance', where the covariance matrix equals rI for the given r (additional parameter). The clustering will have a tendency to divide data into balls with approximate radius proportional to the square root of r.
 "spherical":
Spherical (radial) Gaussian densities (covariance proportional to the identity). Clusters will have a tendency to form balls of arbitrary sizes.
 "diagonal":
Gaussian densities with diagonal covariane. Data will form ellipsoids with radiuses parallel to the coordinate axes.
 "eigenvalues":
Gaussian densities with covariance matrix having fixed eigenvalues (additional parameter). The clustering will try to divide the data into fixedshaped ellipsoids rotated by an arbitrary angle.
 "mean":
Gaussian densities with a fixed mean. Data will be covered with ellipsoids with fixed centers.
The implementation of cec
function allows mixing of clustering types.
Value
An object of class cec
with the following attributes:
data
, cluster
, probability
, centers
,
cost.function
, nclusters
, iterations
, cost
,
covariances
, covariances.model
, time
.
References
Spurek, P. and Tabor, J. (2014) CrossEntropy Clustering Pattern Recognition 47, 9 3046–3059
See Also
CECpackage
, plot.cec
,
print.cec
Examples
## Example of clustering a random data set of 3 Gaussians, with 10 random
## initial centers and a minimal cluster size of 7% of the total data set.
m1 < matrix(rnorm(2000, sd = 1), ncol = 2)
m2 < matrix(rnorm(2000, mean = 3, sd = 1.5), ncol = 2)
m3 < matrix(rnorm(2000, mean = 3, sd = 1), ncol = 2)
m3[,2] < m3[, 2]  5
m < rbind(m1, m2, m3)
plot(m, cex = 0.5, pch = 19)
## Clustering result:
Z < cec(m, 10, iter.max = 100, card.min = "7%")
plot(Z)
# Result:
Z
## Example of clustering mouselike set using spherical Gaussian densities.
m < mouseset(n = 7000, r.head = 2, r.left.ear = 1.1, r.right.ear = 1.1,
left.ear.dist = 2.5, right.ear.dist = 2.5, dim = 2)
plot(m, cex = 0.5, pch = 19)
## Clustering result:
Z < cec(m, 3, type = 'sp', iter.max = 100, nstart = 4, card.min = '5%')
plot(Z)
# Result:
Z
## Example of clustering data set 'Tset' using 'eigenvalues' clustering type.
data(Tset)
plot(Tset, cex = 0.5, pch = 19)
centers < init.centers(Tset, 2)
## Clustering result:
Z < cec(Tset, 5, 'eigenvalues', param = c(0.02, 0.002), nstart = 4)
plot(Z)
# Result:
Z
## Example of using cec split method starting with a single cluster.
data(mixShapes)
plot(mixShapes, cex = 0.5, pch = 19)
## Clustering result:
Z < cec(mixShapes, 1, split = TRUE)
plot(Z)
# Result:
Z