Affiliations: School of Electrical and Electronic Engineering,
Yonsei University, C613, 134 Shinchon-dong, Seodaemun-gu, Seoul, Korea,
120-749 | Department of Electrical and Computer Engineering,
University of Alberta, Edmonton T6R 2G7, Canada and Systems Research Institute,
Polish Academy of Sciences, Warsaw, Poland
Abstract: Fuzzy clustering forms a cornerstone of fuzzy (granular) modeling.
The clusters (prototypes) are viewed as a blueprint of the model that is
further refined through a number of detailed estimation techniques. In this
study, we claim that while clustering is indisputable essential to fuzzy
modeling, the essence of clustering mechanisms supporting this process of
information granulation is not compatible with the character of the task at
hand. In modeling, the required constructs are inherently direction-sensitive
(that is we clearly distinguish between input and output variables). On the
other hand, fuzzy clustering is direction neutral and during the formation of
the clusters does not take this into consideration. We re-formulate the
clustering so that the directionality aspect can be addressed in the
optimization process. This leads to a new, augmented objective function to be
minimized. A detailed algorithm is derived. As the directional sensitivity of
the clustering method gives rise to different numbers of clusters in the input
and output space, it becomes necessary to identify a mapping between these
clusters which in turn gives rise to some allocation problem. Because of its
inherently combinatorial character, the proposed solution is obtained through
some genetic optimization. Comprehensive experiments demonstrate the
performance of the approach and compare it with some of the generic version of
the FCM clustering.
Keywords: Fuzzy clustering, function approximation, genetic algorithm, fuzzy granular modeling, information granulation, fuzzy c-means, directional aspects of clustering
