CSL.IDX {UniversalCVI}

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)

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.

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.

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.

Author(s)

Nathakhun Wiroonsri and Onthada Preedasawakul

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),]