The BYY annealing learning algorithm for Gaussian mixture with automated model selection

Bayesian Ying–Yang (BYY) learning has provided a new mechanism that makes parameter learning with automated model selection via maximizing a harmony function on a backward architecture of the BYY system for the Gaussian mixture. However, since there are a large number of local maxima for the harmony function, any local searching algorithm, such as the hard-cut EM algorithm, does not work well. In order to overcome this difficulty, we propose a simulated annealing learning algorithm to search the global maximum of the harmony function, being expressed as a kind of deterministic annealing EM procedure. It is demonstrated by the simulation experiments that this BYY annealing learning algorithm can efficiently and automatically determine the number of clusters or Gaussians during the learning process. Moreover, the BYY annealing learning algorithm is successfully applied to two real-life data sets, including Iris data classification and unsupervised color image segmentation.