ecm {evclust}

Evidential c-means algorithm

Description

ecm computes a credal partition from a matrix of attribute data using the Evidential c-means (ECM) algorithm.

Usage

ecm(
  x,
  c,
  g0 = NULL,
  type = "full",
  pairs = NULL,
  Omega = TRUE,
  ntrials = 1,
  alpha = 1,
  beta = 2,
  delta = 10,
  epsi = 0.001,
  init = "kmeans",
  disp = TRUE
)

Arguments

x

input matrix of size n x d, where n is the number of objects and d the number of attributes.

c

Number of clusters.

g0

Initial prototypes, matrix of size c x d. If not supplied, the prototypes are initialized randomly.

type

Type of focal sets ("simple": empty set, singletons and Omega; "full": all 2^c subsets of \Omega; "pairs": \emptyset, singletons, \Omega, and all or selected pairs).

pairs

Set of pairs to be included in the focal sets; if NULL, all pairs are included. Used only if type="pairs".

Omega

Logical. If TRUE (default), the whole frame is included (for types 'simple' and 'pairs').

ntrials

Number of runs of the optimization algorithm (set to 1 if m0 is supplied).

alpha

Exponent of the cardinality in the cost function.

beta

Exponent of masses in the cost function.

delta

Distance to the empty set.

epsi

Minimum amount of improvement.

init

Initialization: "kmeans" (default) or "rand" (random).

disp

If TRUE (default), intermediate results are displayed.

Details

ECM is an evidential version algorithm of the Hard c-Means (HCM) and Fuzzy c-Means (FCM) algorithms. As in HCM and FCM, each cluster is represented by a prototype. However, in ECM, some sets of clusters are also represented by a prototype, which is defined as the center of mass of the prototypes in each individual cluster. The algorithm iteratively optimizes a cost function, with respect to the prototypes and to the credal partition. By default, each mass function in the credal partition has 2^c focal sets, where c is the supplied number of clusters. We can also limit the number of focal sets to subsets of clusters with cardinalities 0, 1 and c (recommended if c>=10), or to all or some selected pairs of clusters. If initial prototypes g0 are provided, the number of trials is automatically set to 1.

Value

The credal partition (an object of class "credpart").

Author(s)

Thierry Denoeux (from a MATLAB code written by Marie-Helene Masson).

References

M.-H. Masson and T. Denoeux. ECM: An evidential version of the fuzzy c-means algorithm. Pattern Recognition, Vol. 41, Issue 4, pages 1384–1397, 2008.

See Also

makeF, extractMass, recm, cecm, plot.credpart

Examples

## Clustering of the Four-class dataset
## Not run: 
data(fourclass)
x<-fourclass[,1:2]
y<-fourclass[,3]
clus<-ecm(x,c=4,type='full',alpha=1,beta=2,delta=sqrt(20),epsi=1e-3,disp=TRUE)
plot(clus,X=x,mfrow=c(2,2),ytrue=y,Outliers=TRUE,Approx=2)

## End(Not run)