Fast α-weighted EM learning for neural networks of module mixtures

A class of extended logarithms is used to derive α-weighted EM (α-weighted Expectation and Maximization) algorithms. These extended EM algorithms (WEM's, α-EM's) have been anticipated to outperform the traditional (logarithmic) EM algorithm on the speed. The traditional approach falls into a special case of the new WEM. In this paper, general theoretical discussions are given first. Then, clear-cut evidences that show faster convergence than the ordinary EM approach are given on the case of mixture-of-expert neural networks. This process takes three steps. The first step is to show concrete algorithms. Then, the convergence is theoretically checked. Thirdly, experiments on the mixture-of-expert learning are tried to show the superiority of the WEM. Besides the supervised learning, unsupervised case on a Gaussian mixture is also examined. Faster convergence of the WEM is observed again.