evclust (version 2.0.3)

bpec: Belief Peak Evidential Clustering (BPEC)

Description

bpec computes a credal partition from a matrix of attribute data using the Belief Peak Evidential Clustering (BPEC) algorithm.

Usage

bpec(
  x,
  g,
  type = "full",
  pairs = NULL,
  Omega = TRUE,
  alpha = 1,
  beta = 2,
  delta = 10,
  epsi = 0.001,
  disp = TRUE,
  distance = 1,
  m0 = NULL
)

Value

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

Arguments

x

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

g

Matrix of size c x d of prototypes (the belief peaks).

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').

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.

disp

If TRUE (default), intermediate results are displayed.

distance

Type of distance use: 0=Euclidean, 1=Mahalanobis.

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'.

Author

Thierry Denoeux.

Details

BPEC is identical to ECM, except that the prototypes are computed from delta-Bel graph using function delta_Bel. The ECM algorithm is then run keeping the prototypes fixed. The distance to the prototypes can be the Euclidean disatnce or it can be an adaptive Mahalanobis distance as in the CECM algorithm.

References

Z.-G. Su and T. Denoeux. BPEC: Belief-Peaks Evidential Clustering. IEEE Transactions on Fuzzy Systems, 27(1):111-123, 2019.

See Also

ecm, cecm, delta_Bel

Examples

## Clustering of the Four-class dataset
if (FALSE) {
data(fourclass)
x<-fourclass[,1:2]
y<-fourclass[,3]
DB<-delta_Bel(x,100,0.9)
plot(x,pch=".")
points(DB$g0,pch=3,col="red",cex=2)
clus<-bpec(x,DB$g0,type='pairs',delta=3,distance=1)
plot(clus,x,mfrow=c(2,2))
}