UniversalCVI (version 1.2.0)

CSL.IDX: Chou-Su-Lai (CSL) index

Description

Computes the CSL (C. H. Chou et al., 2004) index for a result either kmeans or hierarchical clustering from user specified kmin to kmax.

Usage

CSL.IDX(x, kmax, kmin = 2, method = "kmeans", nstart = 100)

Value

CSL

the CSL index for k from kmin to kmax shown in a data frame where the first and the second columns are k and the CSL 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.

kmax

a maximum number of clusters to be considered.

kmin

a minimum number of clusters to be considered. The default is 2.

method

a character string indicating which clustering method to be used ("kmeans", "hclust_complete", "hclust_average", "hclust_single"). The default is "kmeans".

nstart

a maximum number of initial random sets for kmeans for method = "kmeans". The default is 100.

Author

Nathakhun Wiroonsri and Onthada Preedasawakul

Details

The CSL index is defined as
$$CSL(k) = \frac{\sum_{i=1}^k \left\{\frac{1}{|C_i|}\sum_{x_j \in C_i} \max_{x_l \in C_i} d(x_j,x_l)\right\}}{\sum_{i=1}^k \left\{\min_{j:j \ne i}d(v_i,v_j)\right\}}. $$ The smallest value of \(CSL(k)\) indicates a valid optimal partition.

References

C. H. Chou, M. C. Su, E. Lai, "A new cluster validity measure and its application to image compression," Pattern Anal Applic, 7, 205-220 (2004).

See Also

Hvalid, Wvalid, DI.IDX, FzzyCVIs, R1_data

Examples

library(UniversalCVI)

# The data is from Wiroonsri (2024).
x = R1_data[,1:2]

# ---- Kmeans ----

# Compute the CSL index
K.CSL = CSL.IDX(scale(x), kmax = 15, kmin = 2, method = "kmeans", nstart = 100)
print(K.CSL)

# The optimal number of cluster
K.CSL[which.min(K.CSL$CSL),]

# ---- Hierarchical ----

# Average linkage

# Compute the CSL index
H.CSL = CSL.IDX(scale(x), kmax = 15, kmin = 2, method = "hclust_average")
print(H.CSL)

# The optimal number of cluster
H.CSL[which.min(H.CSL$CSL),]