fclust (version 2.1.1.1)

NEFRC.noise: Non-Euclidean Fuzzy Relational Clustering with noise cluster

Description

Performs the Non-Euclidean Fuzzy Relational data Clustering algorithm.
The noise cluster is an additional cluster (with respect to the k standard clusters) such that objects recognized to be outliers are assigned to it with high membership degrees.

Usage

NEFRC.noise(D, k, m, delta, RS, startU, index, alpha, conv, maxit, seed)

Value

Object of class fclust, which is a list with the following components:

U

Membership degree matrix

H

Prototype matrix (NULL for NEFRC.noise)

F

Array containing the covariance matrices of all the clusters (NULL for NEFRC.noise)

clus

Matrix containing the indexes of the clusters where the objects are assigned (column 1) and the associated membership degrees (column 2)

medoid

Vector containing the indexes of the medoid objects (NULL for NEFRC.noise)

value

Vector containing the loss function values for the RS starts

criterion

Vector containing the values of the cluster validity index

iter

Vector containing the numbers of iterations for the RS starts

k

Number of clusters

m

Parameter of fuzziness

ent

Degree of fuzzy entropy (NULL for NEFRC.noise)

b

Parameter of the polynomial fuzzifier (NULL for NEFRC.noise)

vp

Volume parameter (NULL for NEFRC.noise)

delta

Noise distance (NULL for NEFRC.noise).

stand

Standardization (Yes if stand=1, No if stand=0) (NULL for NEFRC.noise).

Xca

Data used in the clustering algorithm (NULL for NEFRC.noise), D is used)

X

Raw data (NULL for NEFRC.noise)

D

Dissimilarity matrix

call

Matched call

Arguments

D

Matrix or data.frame containing distances/dissimilarities

k

An integer value or vector specifying the number of clusters for which the index is to be calculated (default: 2:6)

m

Parameter of fuzziness (default: 2)

delta

Noise distance (default: average observed distance)

RS

Number of (random) starts (default: 1)

startU

Rational start for the membership degree matrix U (default: no rational start)

index

Cluster validity index to select the number of clusters: "PC" (partition coefficient), "PE" (partition entropy), "MPC" (modified partition coefficient), "SIL" (silhouette), "SIL.F" (fuzzy silhouette) (default: "SIL.F")

alpha

Weighting coefficient for the fuzzy silhouette index SIL.F (default: 1)

conv

Convergence criterion (default: 1e-9)

maxit

Maximum number of iterations (default: 1e+6)

seed

Seed value for random number generation (default: NULL)

Author

Paolo Giordani, Maria Brigida Ferraro, Alessio Serafini

Details

If startU is given, the argument k is ignored (the number of clusters is ncol(startU)).
If startU is given, the first element of value, cput and iter refer to the rational start.

References

Davé, R. N., & Sen, S. 2002. Robust fuzzy clustering of relational data. IEEE Transactions on Fuzzy Systems, 10(6), 713-727.

See Also

NEFRC, print.fclust, summary.fclust, plot.fclust

Examples

if (FALSE) {
require(cluster)
data("houseVotes")
X <- houseVotes[,-1]
D <- daisy(x = X, metric = "gower")
clust.NEFRC.noise <- NEFRC.noise(D = D, k = 2:6, m = 2, index = "SIL.F")
summary(clust.NEFRC.noise)
plot(clust.NEFRC.noise)
}