An Asymmetric Criterion for Cluster Validation - Developing Concepts in Applied Intelligence - page 11

Before and after applying threshold, the co-association matrix is equal to
equation 7 and 8, respectively

1 1 0 . 0 0

⎡ ⎤

⎢ ⎥

1 1 0 . 0 0

⎢ ⎢ ⎥ ⎥

C = 0 . 5 0 . 5 1 0 . 5 0 5

(7)

before

⎢ ⎢ ⎥ ⎥

0 0 0 . 1 1

⎢ ⎥

0 0 0 . 1 1

⎣ ⎦

In this matrix the 3 rd object can be considered as both clusters with an equal
probability 50%. The stability measure adds some info to this matrix by applying the
threshold.

⎡ 1 1 0 0 0 ⎤

⎢ ⎢ ⎥ ⎥

1 1 0 0 0

⎢ ⎢ ⎥ ⎥

C = 0 0 1 0 5 0 . 5

(7)

after

0 0 0 . 5 1 1

⎢ ⎢ ⎥ ⎥

0 0 0 . 5 1 1

⎣ ⎦

By comparing these two matrices and also considering the stability values, it can be
apprehended that deletion of unstable clusters improves the co-association matrix. In
other hand, eliminating the unstable cluster with samples {1,2,3} which is spuriously
created by primary clusterings, enlightens the matrix.
After erecting the co-association matrix by EEAC method, a consensus function is
employed to extract the final clusters from the matrix. Here, the single-link method is
used for this task.

4 Experimental Results

This section reports and discusses the empirical studies. The proposed method is
examined over 5 different standard datasets. It is tried for datasets to be diverse in
their number of true classes, features and samples. A large variety in used datasets can
more validate the obtained results. Brief information about the used datasets is
available in Table 1.

Table 1. Brief information about the used datasets.

Class Features Samples

Glass 6 9 214

Breast-C 2 9 683

Wine 3 13 178

Bupa 2 6 345

Yeast 10 8 1484