A study of cluster validity criteria for the fuzzy c-regression models clustering algorithm

The fuzzy c-regression models (FCRM) clustering algorithm can fit data to locally regression models which are linear in their parameters and be used as a tool to the identification of complex nonlinear systems. To date, only a few cluster validity criteria have been proposed for the FCRM clustering algorithm to validate the partitions produced by the FCRM clustering algorithm. In this article, we examine the role of a subtle but important parameter - the weighting exponent m - plays in determining the validity of FCRM partitions. The criteria considered are the partition coefficient and two cluster validity criteria we have proposed before. The limit analysis is applied to study the behavior of these cluster validity criteria as mrarr1 and mrarrinfin . It is shown that the proposed cluster validity criteria provide well responses over a wide range of m to choose the correct cluster number.