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

View source: R/kwon.R

kwon	R Documentation

Kwon Index

Description

Computes the Kwon Index (Kwon, 1998) in order to validate the result of a fuzzy and/or possibilistic clustering analysis.

Usage

kwon(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

Kwon Index (I_{Kwon}) is defined as follows:

I_{Kwon}=\frac{∑\limits_{i=1}^n ∑\limits_{j=1}^k u_{ij}^m \; d_{ij}^2 + \frac{1}{k} \; ∑\limits_{j=1}^k ||\vec{v_i}-\bar{v}||^2}{\min\limits_{j\neq l}^k (||\vec{v_j} - \vec{v}_l||^2)}

The optimal clustering is obtained at the minimum value of I_{Kwon}.

Value

`kwon`	Kwon index value if `tidx` is ‘f’
`kwon.e`	extended Kwon index value if `tidx` is ‘e’
`kwon.g`	generalized Kwon index value if `tidx` is ‘g’

Author(s)

Zeynel Cebeci

References

Kwon, S. H. (1998). Cluster validity index for fuzzy clustering. Electronics Letters, 34(22):2176-2177.<10.1049/el:19981523>

Examples

# Load the dataset iris
data(iris)
x <- iris[,1:4]

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

# Compute the Kwon index using res.fcm, which is a ppclust object
idx <- kwon(res.fcm)
print(idx)
 
# Compute the Kwon index using X, U and V matrices
idx <- kwon(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 Kwon index using res.upfc, which is a ppclust object
idx <- kwon(res.upfc, tidx="g")
print(idx)

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