pbm: Pakhira-Bandyopadhyay-Maulik Index
In zcebeci/fcvalid: Internal Validity Indexes for Fuzzy and Possibilistic Clustering

View source: R/pbm.R

pbm	R Documentation

Pakhira-Bandyopadhyay-Maulik Index

Description

Computes the Pakhira-Bandyopadhyay-Maulik (Pakhira et al, 2005) index for validating the result of a fuzzy and/or possibilistic clustering analysis.

Usage

pbm(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’.
`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’.
`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 Pakhira-Bandyopadhyay-Maulik (PBM) index proposed by Pakhira et al (2005) has two versions which can be used for validating both hard and soft clustering results. The formula in the following equation is the fuzzy version PBM index so-called PBMF in some of the literature:

I_{PBM}=\frac{1}{k} \;\frac{E_0}{E_k} \; D_k

Where: E_0 = ∑\limits_{i=1}^n ||x_i-\bar{v}||^2, E_k = ∑\limits_{j=1}^k E_j, E_j = ∑\limits_{j=1}^k u_{ij} \; d_{ij}^2, D_k = \max\limits_{j,l=1}^k ||\vec{v}_j-\vec{v}_l||^2

The optimal clustering is obtained with the maximum value of I_{PBM}.

Value

`pbm`	PBM index value, if `tidx` is ‘f’
`pbm.e`	extended PBM index value, if `tidx` is ‘e’
`pbm.g`	generalized PBM index value, if `tidx` is ‘g’

Author(s)

Zeynel Cebeci

References

Pakhira, M.K., Bandyopadhyay, S. & Maulik, U. (2005). Validity index for crisp and fuzzy clusters, Pattern Recognition, 37(3):487-501. <doi:10.1016/j.patcog.2003.06.005>

Examples

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

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

# Compute the PBM index using ppclust object
idx <- pbm(res.fcm)
print(idx)
 
# Compute the PBM index using X,U,V matrices
idx <- pbm(res.fcm$x, res.fcm$u, res.fcm$v, m=2)
print(idx)

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