An Asymmetric Criterion for Cluster Validation - Developing Concepts in Applied Intelligence - page 9

ab
ij

*

where n is number of samples available in the cluster C i and

n

denotes the number

a
i

a b

j

* b *

of shared samples between the clusters

C ∈ P

and

C ∈ P

. Also k b* is the number

of clusters in P b* .

b*

Fig. 6. Computing the entropy between the cluster C 1 from P a and P b* from P b .

Here, the Average APMM, AAPMM is proposed as a measure of stability of a
primary cluster C i with respect to the partitions available in the reference set as
equation 4:

1

M

∑
=

a
i

b
j

*

AAPMM ( C ) = APMM ( C , P )

(4)

i

M

j 1

b

where

P

is from j -th partition of the reference set.

3.2 Extended EAC (EEAC)

In this step, the selected clusters have to construct the co-association matrix. In EAC
method the m primary results from resampled data are accumulated in an n×n co-
association matrix. Each entry in this matrix is computed from equation 5.

n

i
m

, j

C ( i , j ) =

(5)

i , j

Where n ij counts the number of clusters shared by objects with indices i and j in the
partitions over the B clusterings. Also m ij is the number of partitions where this pair of
objects is simultaneously present. There are only a fraction of all primary clusters
available, after Thresholding. So, the common EAC method cannot truly recognize