PBM.IDX {UniversalCVI} | R Documentation |
Pakhira-Bandyopadhyay-Maulik (PBM) index
Description
Computes the PBM (M. K. Pakhira et al., 2004) index for a result of either FCM or EM clustering from user specified cmin
to cmax
.
Usage
PBM.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 |
method |
a character string indicating which clustering method to be used ( |
fzm |
a number greater than 1 giving the degree of fuzzification for |
nstart |
a maximum number of initial random sets for FCM for |
iter |
a maximum number of iterations for |
Details
The PBM index is defined as
PBM(c) = \left(\frac{\sum_{i=1}^n \| {x}_i-{v}_0\| \cdot \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 PBM(c)
indicates a valid optimal partition.
Value
PBM |
the PBM index for |
Author(s)
Nathakhun Wiroonsri and Onthada Preedasawakul
References
M. K. Pakhira, S. Bandyopadhyay, and U. Maulik, “Validity index for crisp and fuzzy clusters,” Pattern recognition, vol. 37, no. 3, pp. 487–501, 2004.
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 PBM index
FCM.PBM = PBM.IDX(scale(x), cmax = 15, cmin = 2, method = "FCM",
fzm = 2, nstart = 20, iter = 100)
print(FCM.PBM)
# The optimal number of cluster
FCM.PBM[which.max(FCM.PBM$PBM),]
# ---- EM algorithm ----
# Compute the PBM index
EM.PBM = PBM.IDX(scale(x), cmax = 15, cmin = 2, method = "EM",
nstart = 20, iter = 100)
print(EM.PBM)
# The optimal number of cluster
EM.PBM[which.max(EM.PBM$PBM),]