General C-means clustering model

Partitional clustering is an important part of cluster analysis. Based on various theories, numerous clustering algorithms have been developed, and new clustering algorithms continue to appear in the literature. It is known that Occam's razor plays a pivotal role in data-based models, and partitional clustering is categorized as a data-based model. However, no relation had previously been discovered between Occam's razor and partitional clustering, as we discuss in this paper. The three main contributions of this paper can be summarized as follows: 1) According to a novel definition of the mean, a unifying generative framework for partitional clustering algorithms, called a general c-means clustering model (GCM), is presented and studied. 2) Based on the local optimality test of the GCM, the connection between Occam's razor and partitional clustering is established for the first time. As its application, a comprehensive review of the existing objective function-based clustering algorithms is presented based on GCM. 3) Under a common assumption about partitional clustering, a theoretical guide for devising and implementing clustering algorithm is discovered. These conclusions are verified by numerical experimental results.