Bayesian Ying-Yang machine, clustering and number of clusters

It is shown that a particular case of the Bayesian Ying-Yang learning system and theory reduces to the maximum likelihood learning of a finite mixture, from which we have obtained not only the EM algorithm for its parameter estimation and its various approximate but fast algorithms for clustering in general cases (including Mahalanobis distance clustering or elliptic clustering), but also criteria for the selection of the number of densities in a mixture, and the number k in the conventional Mean Square Error clustering. Moreover, a Re-weighted EM algorithm is also proposed and shown to be more robust in learning. Finally, experimental results are provided. (C) 1997 Elsevier Science B.V.