fcvalid: Internal Validity Indexes for Fuzzy and Possibilistic Clustering

View source: R/cs.R

cs	R Documentation

Compactness / Separation Ratio

Description

Computes the Separation/Compactness (Bensaid et al, 1996) ratio index in order to validate the result of a fuzzy and/or possibilistic clustering analysis.

Usage

cs(x, u, v, m, t=NULL, eta, tidx="f")

Arguments

`x`	an object of class ‘ppclust’ containing the clustering results from a fuzzy clustering algorithm in the package ppclust. Alternatively, a numeric data frame or matrix containing the data set.
`u`	a numeric data frame or matrix containing the fuzzy membership values. It should be specified if `x` is not an object of ‘ppclust’.
`v`	a numeric data frame or matrix containing the cluster prototypes. It should be specified if `x` is not an object of ‘ppclust’.
`t`	a numeric data frame or matrix containing the cluster prototypes. It should be specified if `x` is not an object of ‘ppclust’ and the option e or g is assigned to `tidx`.
`m`	a number specifying the fuzzy exponent. It should be specified if `x` is not an object of ‘ppclust’.
`eta`	a number specifying the typicality exponent. It should be specified if `x` is not an object of ‘ppclust’ and `tidx` is either e or g.
`tidx`	a character specifying the type of index. The default is ‘f’ for fuzzy index. The other options are ‘e’ for extended and ‘g’ for generalized index.

Details

The validity-guided (re)clustering (VGC) algorithm uses cluster-validity information to guide a fuzzy (re)clustering process toward better solutions. It starts with a partition generated by a soft or fuzzy clustering algorithm. Then it iteratively alters the partition by applying split-and-merge operations to the clusters (Bensaid, 1996). The authors proposed the Compactness / Separation (CS) ratio index in order to validate the results of VGC. The formula of CS index is:

I_{CS}=∑\limits_{j=1}^k \frac{∑\limits_{i=1}^n u_{ij}^m \; d_{ij}^2}{∑\limits_{i=1}^n u_{ij} \; ∑\limits_{l=1}^k||\vec{v_j} - \vec{v_l}||^2}

A lower value of I_{CS} indicates a better clustering.

Value

`cs`	CS index value if `tidx` is ‘f’
`cs.e`	extended CS index value if `tidx` is ‘e’
`cs.g`	generalized CS index value if `tidx` is ‘g’

Author(s)

Zeynel Cebeci

References

Bensaid, A.M., Hall, L.O., Bezdek, J.C., Clarke, L.P., Silbiger, M.L., Arrington, J.A. & Murtagh, R.F. (1996). Validity-guided (re)clustering with applications to image segmentation, IEEE Transactions on Fuzzy Systems, 4(2):112-123. <10.1109/91.493905>

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 CS index using res.fcm, which is a ppclust object
idx <- cs(res.fcm)
print(idx)
 
# Compute the CS index using X, U and V matrices
idx <- cs(res.fcm$x, res.fcm$u, res.fcm$v)
print(idx)

# Run UPFCM algorithm in the package ppclust 
res.upfc <- ppclust::upfc(x, centers=3)
# Compute the generalized CS index using res.upfc, which is a ppclust object
idx <- cs(res.upfc, tidx="g")
print(idx)

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