KPBM.IDX {UniversalCVI}

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)

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.

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.

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.

Author(s)

Nathakhun Wiroonsri and Onthada Preedasawakul

References

C. Alok. (2010). "An investigation of clustering algorithms and soft computing approaches for pattern recognition," Department of Computer Science, Assam University. http://hdl.handle.net/10603/93443

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),]