DI.IDX {UniversalCVI}

Dunn index

Description

Computes the DI (J. C. Dunn, 1973) index for a result either kmeans or hierarchical clustering from user specified kmin to kmax.

Usage

DI.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 DI index is defined as

DI(k) = \min_{i \ne j \in [k]}\left\{\frac{\min\left\{d(x_u,x_v)|x_u\in C_i,x_v \in C_j\right\}}{\max_{l \in [k]}\max\left\{d(x_u,x_v)|x_u,x_v \in C_l\right\}}\right\}.

The largest value of DI(k) indicates a valid optimal partition.

Value

DI

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

Author(s)

Nathakhun Wiroonsri and Onthada Preedasawakul

References

J. C. Dunn, "A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters," J Cybern, 3(3), 32-57 (1973).

See Also

Hvalid, Wvalid, DB.IDX, FzzyCVIs, R1_data

Examples

library(UniversalCVI)

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

# ---- Kmeans ----

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

# The optimal number of cluster
K.DI[which.max(K.DI$DI),]

# ---- Hierarchical ----

# Average linkage

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

# The optimal number of cluster
H.DI[which.max(H.DI$DI),]