General c-means clustering model and its application

Many partitional clustering algorithms originated from the definition of mean.We propose a new clustering model - general c-means clustering algorithm (GCM). Generally, when the data set is clustered into c (c > 1) subsets, each subset is often expected to have a different prototype (or cluster center) than others. Therefore, we propose the definition of undesirable solution of clustering algorithms. As the GCM has undesirable solution under a mild condition, undesirable solution of the GCM is not expected to be stable. According to these assumptions, we obtain the necessary conditions for the GCM as a good clustering model. Fortunately, such conditions have offered a theoretical basis for selection of the parameters in many clustering algorithms, which is an open problem for such algorithms, for example, we get the theoretical rule for selection of the weighting exponent in the FCM, and explain why the weighting exponent should be greater than 1, etc. Moreover, we discover the relation between the GCM model and Occam´s razor, which offers the deep reason behind many famous partitional clustering algorithms. Based on these results, we can study many objective function based clustering algorithms.