XB.IDX: Xie and Beni (XB) index
| XB.IDX | R Documentation |
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 |
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 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 |
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),]
