DB.IDX {UniversalCVI}

Davies–Bouldin (DB) and DB* (DBs) indexes

Description

Computes the DB (D. L. Davies and D. W. Bouldin, 1979) and DBs (M. Kim and R. S. Ramakrishna, 2005) indexes for a result either kmeans or hierarchical clustering from user specified kmin to kmax.

Usage

DB.IDX(x, kmax, kmin = 2, method = "kmeans",
  indexlist = "all", p = 2, q = 2, 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".

indexlist

a character string indicating which cluster validity indexes to be computed ("all", "DB", "DBs"). More than one indexes can be selected.

p

the power of the Minkowski distance between centroids of clusters. The default is 2.

q

the power of dispersion measure of a cluster. The default is 2.

nstart

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

Details

The lowest value of DB(k),DBs(k) indicates a valid optimal partition.

Value

DB

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

DBs

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

Author(s)

Nathakhun Wiroonsri and Onthada Preedasawakul

References

D. L. Davies, D. W. Bouldin, "A cluster separation measure," IEEE Trans Pattern Anal Machine Intell, 1, 224-227 (1979).

M. Kim, R. S. Ramakrishna, "New indices for cluster validity assessment," Pattern Recognition Letters, 26, 2353-2363 (2005).

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 all the indices by DB.IDX
K.ALL = DB.IDX(scale(x), kmax = 15, kmin = 2, method = "kmeans",
  indexlist = "all", p = 2, q = 2, nstart = 100)
print(K.ALL)

# Compute DB index
K.DB = DB.IDX(scale(x), kmax = 15, kmin = 2, method = "kmeans",
  indexlist = "DB", p = 2, q = 2, nstart = 100)
print(K.DB)

# ---- Hierarchical ----

# Average linkage

# Compute all the indices by DB.IDX
H.ALL = DB.IDX(scale(x), kmax = 15, kmin = 2, method = "hclust_average",
  indexlist = "all", p = 2, q = 2)
print(H.ALL)

# Compute DB index
H.DB = DB.IDX(scale(x), kmax = 15, kmin = 2, method = "hclust_average",
  indexlist = "DB", p = 2, q = 2)
print(H.DB)