awcd: Average Within-Cluster Distance
In zcebeci/fcvalid: Internal Validity Indexes for Fuzzy and Possibilistic Clustering

View source: R/awcd.R

awcd	R Documentation

Average Within-Cluster Distance

Description

Computes the Average Within-Cluster Distance (Krishnapuram & Freg, 1992) to validate the result of a fuzzy and/or possibilistic clustering analysis.

Usage

awcd(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

Average Within-Cluster Distance (AWCD) is defined as:

I_{AWCD}=\frac{1}{n \; k} \frac{∑\limits_{i=1}^n u_{ij}^m \; d_{ij}^2}{∑\limits_{i=1}^n u_{ij}^m}

As the I_{AWCD} monotonically decreases with the number of clusters. A knee in the curve of I_{AWCD} as a function of k indicates a good fuzzy partition.

Value

`awcd`	AWCD index value if `tidx` is ‘f’
`awcd.e`	extended AWCD index value if `tidx` is ‘e’
`awcd.g`	generalized AWCD index value if `tidx` is ‘g’

Author(s)

Zeynel Cebeci

References

Krishnapuram, R. & Freg, C. P. (1992). Fitting an unknown number of lines and planes to image data through compatible cluster merging. Pattern Recognition, 25(4):385-400. <doi:10.1016/0031-3203(92)90087-Y>

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

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