recm: Relational Evidential c-means algorithm

In evclust: Evidential Clustering

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
)

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.

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.

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. 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
## Not run: 
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)
 
## End(Not run)

evclust documentation built on Nov. 9, 2023, 5:05 p.m.