evclust (version 2.0.3)

recm: Relational Evidential c-means algorithm

Description

recm computes a credal partition from a dissimilarity matrix using the Relational Evidential c-means (RECM) algorithm.

Usage

recm(
  D,
  c,
  type = "full",
  pairs = NULL,
  Omega = TRUE,
  m0 = NULL,
  ntrials = 1,
  alpha = 1,
  beta = 1.5,
  delta = quantile(D[upper.tri(D) | lower.tri(D)], 0.95),
  epsi = 1e-04,
  maxit = 5000,
  disp = TRUE
)

Value

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

Arguments

D

Dissimilarity matrix of size (n,n), where n is the number of objects. Dissimilarities must be squared Euclidean distances to ensure convergence.

c

Number of clusters.

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').

m0

Initial credal partition. Should be a matrix with n rows and a number of columns equal to the number f of focal sets specified by 'type' 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.

maxit

Maximum number of iterations.

disp

If TRUE (default), intermediate results are displayed.

Author

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

Details

RECM is a relational version of the Evidential c-Means (ECM) algorithm. Convergence is guaranteed only if elements of matrix D are squared Euclidean distances. However, the algorithm is quite robust and generally provides sensible results even if the dissimilarities are not metric. 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 an initial credal partition m0 is provided, the number of trials is automatically set to 1.

References

M.-H. Masson and T. Denoeux. RECM: Relational Evidential c-means algorithm. Pattern Recognition Letters, Vol. 30, pages 1015--1026, 2009.

See Also

makeF, extractMass, ecm

Examples

## Clustering of the Butterfly dataset
if (FALSE) {
n <- nrow(butterfly)
D<-as.matrix(dist(butterfly))^2
clus<-recm(D,c=2,delta=sqrt(50))
m<-clus$mass
plot(1:n,m[,1],type="l",ylim=c(0,1),xlab="objects",ylab="masses")
lines(1:n,m[,2],lty=2)
lines(1:n,m[,3],lty=3)
lines(1:n,m[,4],lty=4)

 ## Clustering the protein data
 data(protein)
 clus <- recm(D=protein$D,c=4,type='full',alpha=0.2,beta=1.1,delta=sqrt(20))

 z<- cmdscale(protein$D,k=2)
 plot(clus,X=z,mfrow=c(2,2),ytrue=protein$y,Outliers=FALSE,Approx=1)
 }