mcd: Minimum Centroid Distance

In zcebeci/fcvalid: Internal Validity Indexes for Fuzzy and Possibilistic Clustering

Minimum Centroid Distance

Description

Computes the Minimum Centroid Distance (MCD) to test the result of a fuzzy clustering analysis (Schwaemmle & Jensen, 2010).

Usage

mcd(x)

Arguments

x	an object of class ‘ppclust’ containing the clustering results from a fuzzy and/or possibilistic clustering algorithm in the package ppclust. Alternatively, it is a numeric data frame or matrix containing the cluster prototypes.

Details

MCD values for different numbers of clusters (k) and different values of fuzzy exponent (m) can be used to compare the results of fuzzy cluster analysis in order find the optimal result. The formula of MCD is:

I_{MCD}=\min\limits_{j \neq l}(||\vec{v_j}-\vec{v_l}||^2)

The optimal clustering is found at the maximum value of MCD.

Value

mcd	MCD value.

Author(s)

Zeynel Cebeci

References

Schwaemmle, V. & Jensen, O.N. (2010). A simple and fast method to determine the parameters for fuzzy c-means cluster validation. <arXiv:http://arxiv.org/abs/1004.1307v1>

See Also

allindexes, apd, cl, cs, cwb, fhv, fs, kpbm, kwon, mpc, pbm, pc, pe, sc, si, tss, ws, xb

Examples

# Load the dataset iris and use the first four feature columns 
data(iris)
x <- iris[,1:4]

# Run FCM algorithm in the package ppclust 
res.fcm <- ppclust::fcm(x, centers=3)

# Compute the MCD using res.fcm, which is a ppclust object
idx <- mcd(res.fcm)
print(idx)
 
# Compute the MCD index using V matrix
idx <- mcd(res.fcm$v)
print(idx)

zcebeci/fcvalid documentation built on Oct. 4, 2022, 9:01 p.m.