UniversalCVI (version 1.2.0)

KPBM.IDX: Modified Kernel form of Pakhira-Bandyopadhyay-Maulik (KPBM) index

Description

Computes the KPBM (C. Alok, 2010) index for a result of either FCM or EM clustering from user specified cmin to cmax.

Usage

KPBM.IDX(x, cmax, cmin = 2, method = "FCM", fzm = 2, nstart = 20, iter = 100)

Value

KPBM

the KPBM index for c from cmin to cmax shown in a data frame where the first and the second columns are c and the KPBM index, respectively.

Arguments

x

a numeric data frame or matrix where each column is a variable to be used for cluster analysis and each row is a data point.

cmax

a maximum number of clusters to be considered.

cmin

a minimum number of clusters to be considered. The default is 2.

method

a character string indicating which clustering method to be used ("FCM" or "EM"). The default is "FCM".

fzm

a number greater than 1 giving the degree of fuzzification for method = "FCM". The default is 2.

nstart

a maximum number of initial random sets for FCM for method = "FCM". The default is 20.

iter

a maximum number of iterations for method = "FCM". The default is 100.

Author

Nathakhun Wiroonsri and Onthada Preedasawakul

Details

The KPBM index is defined as
$$KPBM(c) = \left(\frac{\max_{j \neq k}\| {v}_j-{v}_k\|}{c\sum_{j=1}^c\sum_{i=1}^n\mu_{ij}\| {x}_i-{v}_j\|}\right)^2.$$ The largest value of \(KPBM(c)\) indicates a valid optimal partition.

References

C. Alok. (2010). "An investigation of clustering algorithms and soft computing approaches for pattern recognition", Department of Computer Science, Assam University.

See Also

R1_data, TANG.IDX, FzzyCVIs, WP.IDX, Hvalid

Examples

library(UniversalCVI)

# The data is from Wiroonsri (2024).
x = R1_data[,1:2]

# ---- FCM algorithm ----

# Compute the KPBM index
FCM.KPBM = KPBM.IDX(scale(x), cmax = 15, cmin = 2, method = "FCM",
  fzm = 2, nstart = 20, iter = 100)
print(FCM.KPBM)

# The optimal number of cluster
FCM.KPBM[which.max(FCM.KPBM$KPBM),]

# ---- EM algorithm ----

# Compute the KPBM index
EM.KPBM = KPBM.IDX(scale(x), cmax = 15, cmin = 2, method = "EM",
  nstart = 20, iter = 100)
print(EM.KPBM)

# The optimal number of cluster
EM.KPBM[which.max(EM.KPBM$KPBM),]