EM algorithms for Gaussian mixtures with split-and-merge operation

摘要

In order to alleviate the problem of local convergence of the usual EM algorithm, a split-and-merge operation is introduced into the EM algorithm for Gaussian mixtures. The split-and-merge equations are first presented theoretically. These equations show that the merge operation is a well-posed problem, whereas the split operation is an ill-posed problem because it is the inverse procedure of the merge. Two methods for solving this ill-posed problem are developed through the singular value decomposition and the Cholesky decomposition. Accordingly, a new modified EM algorithm is constructed. Our experiments demonstrate that this algorithm is efficient for unsupervised color image segmentation.