XB.IDX {UniversalCVI}

Xie and Beni (XB) index

Description

Computes the XB (X. L. Xie and G. Beni, 1991) index for a result of either FCM or EM clustering from user specified cmin to cmax.

Usage

XB.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 XB index is defined as

XB(c) = \frac{\sum_{j=1}^c\sum_{i=1}^n\mu_{ij}^2\| {x}_i-{v}_j\|^2} {n \cdot \min_{j\neq k} \{ \| {v}_j-{v}_k\|^2 \}}.

The lowest value of XB(c) indicates a valid optimal partition.

Value

XB

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

Author(s)

Nathakhun Wiroonsri and Onthada Preedasawakul

References

X. Xie and G. Beni, “A validity measure for fuzzy clustering,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 8, pp. 841–847, 1991.

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

# The optimal number of cluster
FCM.XB[which.min(FCM.XB$XB),]

# ---- EM algorithm ----

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

# The optimal number of cluster
EM.XB[which.min(EM.XB$XB),]