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

✍ Scribed by Zhihua Zhang; Chibiao Chen; Jian Sun; Kap Luk Chan

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 794 KB
Volume: 36
Category: Article
ISSN: 0031-3203
DOI: 10.1016/s0031-3203(03)00059-1

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✦ Synopsis

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 ÿrst 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 modiÿed EM algorithm is constructed. Our experiments demonstrate that this algorithm is e cient for unsupervised color image segmentation.

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