TANG.IDX {UniversalCVI}

Tang index

Description

Computes the TANG (Y. Tang et al., 2005) index for a result of either FCM or EM clustering from user specified cmin to cmax.

Usage

TANG.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 Tang index is defined as

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

The smallest value of TANG(c) indicates a valid optimal partition.

Value

TANG

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

Author(s)

Nathakhun Wiroonsri and Onthada Preedasawakul

References

Y. Tang, F. Sun, and Z. Sun, “Improved validation index for fuzzy clustering,” in Proceedings of the 2005, American Control Conference, 2005., pp. 1120–1125 vol. 2, 2005. https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1470111&isnumber=31519

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

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

# ---- EM algorithm ----

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

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