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

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 prob...

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Bibliographic Details
Published inPattern recognition Vol. 36; no. 9; pp. 1973 - 1983
Main Authors Zhang, Zhihua, Chen, Chibiao, Sun, Jian, Luk Chan, Kap
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2003
Subjects
EM algorithms
Gaussian mixtures
Image segmentation
Split-and-merge operation
Statistical computer vision
Statistical computer vision
Image segmentation
Split-and-merge operation
Gaussian mixtures
EM algorithms
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Summary: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.
ISSN:0031-3203
1873-5142
DOI:10.1016/S0031-3203(03)00059-1