KWON2.IDX {UniversalCVI}

KWON2 index

Description

Computes the KWON2 (S. H. Kwon et al., 2021) index for a result of either FCM or EM clustering from user specified cmin to cmax.

Usage

KWON2.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

KWON2 is defined as

KWON2(c) = \frac{w_1\left[w_2\sum_{j=1}^c\sum_{i=1}^n \mu_{ij}^{2^{\sqrt{\frac{m}{2}}}} \|{x}_i-{v}_j\|^2 + \frac{\sum_{j=1}^c\| {v}_j-{v}_0\|^2}{\max_j \|{v}_j-{v}_0\|^2 } + w_3 \right]}{\min_{i \neq j} \| {v}_i-{v}_j\|^2 + \frac{1}{c}+\frac{1}{c^m-1}}.

where w_1 = \frac{n-c+1}{n}, w_2 = \left(\frac{c}{c-1}\right)^{\sqrt{2}} and w_3=\frac{nc}{(n-c+1)^2}.

The smallest value of KWON2(c) indicates a valid optimal partition.

Value

KWON2

the KWON2 index for c from cmin to cmax shown in a data frame where the first and the second columns are c and the KWON2 index, respectively.

Author(s)

Nathakhun Wiroonsri and Onthada Preedasawakul

References

S. H. Kwon, J. Kim, and S. H. Son, “Improved cluster validity index for fuzzy clustering,” Electronics Letters, vol. 57, no. 21, pp. 792–794, 2021.

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 KWON2 index
FCM.KWON2 = KWON2.IDX(scale(x), cmax = 15, cmin = 2, method = "FCM",
  fzm = 2, nstart = 20, iter = 100)
print(FCM.KWON2)

# The optimal number of cluster
FCM.KWON2[which.min(FCM.KWON2$KWON2),]

# ---- EM algorithm ----

# Compute the KWON2 index
EM.KWON2 = KWON2.IDX(scale(x), cmax = 15, cmin = 2, method = "EM",
  nstart = 20, iter = 100)
print(EM.KWON2)

# The optimal number of cluster
EM.KWON2[which.min(EM.KWON2$KWON2),]