Two Further Gradient BYY Learning Rules for Gaussian Mixture with Automated Model Selection

Under the Bayesian Ying-Yang (BYY) harmony learning theory, a harmony function has been developed for Gaussian mixture model with an important feature that, via its maximization through a gradient learning rule, model selection can be made automatically during parameter learning on a set of sample data from a Gaussian mixture. This paper proposes two further gradient learning rules, called conjugate and natural gradient learning rules, respectively, to efficiently implement the maximization of the harmony function on Gaussian mixture. It is demonstrated by simulation experiments that these two new gradient learning rules not only work well, but also converge more quickly than the general gradient ones.