WL.IDX {UniversalCVI}

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)

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 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.

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.

Author(s)

Nathakhun Wiroonsri and Onthada Preedasawakul

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),]