FKM.med.noise {fclust}

Fuzzy k-medoids with noise cluster

Description

Performs the fuzzy k-medoids clustering algorithm with noise cluster.
Differently from fuzzy k-means where the cluster prototypes (centroids) are artificial objects computed as weighted means, in the fuzzy k-medoids the cluster prototypes (medoids) are a subset of the observed objects.
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

 
 FKM.med.noise (X, k, m, delta, RS, stand, startU, index, alpha, conv, maxit, seed)

Arguments

X

Matrix or data.frame

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: 1.5)

delta

Noise distance (default: average Euclidean distance between objects and prototypes from FKM.med using the same values of k and m)

RS

Number of (random) starts (default: 1)

stand

Standardization: if stand=1, the clustering algorithm is run using standardized data (default: no standardization)

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), XB (Xie and Beni) (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)

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.
As for FKM.med, in FKM.med.noise the parameter of fuzziness is usually lower than the one used in FKM.

Value

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

U

Membership degree matrix

H

Prototype matrix

F

Array containing the covariance matrices of all the clusters (NULL for FKM.med.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

value

Vector containing the loss function values for the RS starts

criterion

Vector containing the values of clustering 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 FKM.med.noise)

b

Parameter of the polynomial fuzzifier (NULL for FKM.med.noise)

vp

Volume parameter (NULL for FKM.med.noise)

delta

Noise distance

gam

Weighting parameter for the fuzzy covariance matrices (NULL for FKM.med.noise)

mcn

Maximum condition number for the fuzzy covariance matrices (NULL for FKM.med.noise)

stand

Standardization (Yes if stand=1, No if stand=0)

Xca

Data used in the clustering algorithm (standardized data if stand=1)

X

Raw data

D

Dissimilarity matrix (NULL for FKM.med.noise)

call

Matched call

Author(s)

Paolo Giordani, Maria Brigida Ferraro, Alessio Serafini

References

Dave' R.N., 1991. Characterization and detection of noise in clustering. Pattern Recognition Letters, 12, 657-664.
Krishnapuram R., Joshi A., Nasraoui O., Yi L., 2001. Low-complexity fuzzy relational clustering algorithms for web mining. IEEE Transactions on Fuzzy Systems, 9, 595-607.

See Also

FKM.med, Fclust, Fclust.index, print.fclust, summary.fclust, plot.fclust, butterfly

Examples

## butterfly data
data(butterfly)
## fuzzy k-medoids with noise cluster, fixing the number of clusters
clust=FKM.med.noise(butterfly,k=2,RS=5,delta=3)
## fuzzy k-medoids with noise cluster, selecting the number of clusters
clust=FKM.med.noise(butterfly,RS=5,delta=3)