Asymptotic Convergence Rate of the EM Algorithm for Gaussian Mixtures
Neural Computation
On the Lower Bound of Local Optimums in K-Means Algorithm
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
On convergence properties of the em algorithm for gaussian mixtures
Neural Computation
Fast mining and forecasting of complex time-stamped events
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Random swap EM algorithm for Gaussian mixture models
Pattern Recognition Letters
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EM algorithm is a very popular iteration-based method to estimate the parameters of Gaussian Mixture Model from a large observation set. However, in most cases, EM algorithm is not guaranteed to converge to the global optimum. Instead, it stops at some local optimums, which can be much worse than the global optimum. Therefore, it is usually required to run multiple procedures of EM algorithm with different initial configurations and return the best solution. To improve the efficiency of this scheme, we propose a new method which can estimate an upper bound on the logarithm likelihood of the local optimum, based on the current configuration after the latest EM iteration. This is accomplished by first deriving some region bounding the possible locations of local optimum, followed by some upper bound estimation on the maximum likelihood. With this estimation, we can terminate an EM algorithm procedure if the estimated local optimum is definitely worse than the best solution seen so far. Extensive experiments show that our method can effectively and efficiently accelerate conventional multiple restart EM algorithm.