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At first, the original Objective Cluster Analysis (OCA) algorithm [7] is im-
proved, incorporated with the Fuzzy
c
-Means (FCM) algorithm [8] and the Least
Square Estimation (LSE) approach [2]. Thus the redundant rules are simplified
effectively and the concise initial rule base is gained. Besides, in the proposed
Enhanced Objective Cluster Analysis (EOCA) method, the Dipole Partition
(DP), the introducing of the Relative Dissimilarity Measure (RDM) [9] and the
presented Enhanced Consistency Criterion (ECC) are used to increase the ro-
bustness of OCA algorithm. Thus the proper accuracy of the initial Mamdani
model is guaranteed. Following, the (1+1) Evolutionary Strategy (ES) [10] is
adopted to optimize the initial parameters. During the evolutionary learning
process, the fitness function is designed by the combination of two constraints,
the Covering Criteria (CC) and the Genetic Niching Principle (GNP). So the
compatibility among the rules and the appropriate over-lapping between the
fuzzy sets could be considered simultaneously. The example of Box-Jenkins [11]
and electrical application [6] demonstrate the compactness, distinguishability
and the moderate accuracy of the presented model.
2
Initial Fuzzy Partitioning via EOCA
By means of the result of EOCA, the initial clustering result is gained and
afforded for Fuzzy
c
-Means (FCM) clustering [8] to form the initial fuzzy parti-
tion [1-4].
Fig. 1.
EOCA principle
The principle of EOCA is shown in Fig.1 and described as follows.
Step 1:
Partition the sample set
Z
into subset
Z
A
and
Z
B
by dipoles.
Step 2:
Execute hierarchical clustering on
Z
A
and
Z
B
, respectively, then obtain
c
AB
and
V
AB
by minimum enhanced consistency index
η
AB
; In the similar way,
obtain
c
CD
and
V
CD
by
η
CD
from
Z
C
and
Z
D
.
Step 3:
Determine the final clustering number
c
E
and the vector of clusters
centers
V
E
from
by selecting the minimum between
η
AB
and
η
CD
. Then the algorithm is completed.
{
c
AB
,V
AB
}
and
{
c
CD
,V
CD
}
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