UniversalCVI (version 1.2.0)

WL.IDX: Wu and Li (WL) index

Description

Computes the WL (C. H. Wu et al., 2015) index for a result of either FCM or EM clustering from user specified cmin to cmax.

Usage

WL.IDX(x, cmax, cmin = 2, method = "FCM", fzm = 2, nstart = 20, iter = 100)

Value

WL

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

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.

Author

Nathakhun Wiroonsri and Onthada Preedasawakul

Details

The WL index is defined as
$$WL(c) = \frac{\sum_{j=1}^c\left(\frac{\sum_{i=1}^n\mu_{ij}^2\| {x}_i-{v}_j\|^2}{\sum_{i=1}^n\mu_{ij}}\right)}{min_{j \neq k}\{\| {v}_j-{v}_k\|^2\} +median_{j \neq k }\{\| {v}_j-{v}_k\|^2\}}.$$ The smallest value of \(WL(c)\) indicates a valid optimal partition.

References

C. H. Wu, C. S. Ouyang, L. W. Chen, and L. W. Lu, “A new fuzzy clustering validity index with a median factor for centroid-based clustering,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 3, pp. 701–718, 2015.https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6811211&isnumber=7115244

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

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

# ---- EM algorithm ----

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

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