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Semi-EM algorithm for solving Gamma mixture model of multimodal probability distribution
Jiaqi CHEN, Yulin HE, Yingchao CHENG, Zhexue HUANG
Journal of Computer Applications    2025, 45 (7): 2153-2161.   DOI: 10.11772/j.issn.1001-9081.2024070942
Abstract15)   HTML0)    PDF (4261KB)(4)       Save

Expectation-Maximization (EM) algorithm plays an important role in parameter estimation for mixture models. However, the existing EM algorithms for solving Gamma Mixture Model (GaMM) parameters have limitations, which mainly are the problems of low-quality parameter estimation led by approximate calculations and inefficient computation due to many numerical calculations. To address these limitations and fully exploit the multimodal nature of data, a Semi-EM algorithm was proposed to solve GaMM for estimating multimodal probability distributions. Firstly, spatial distribution characteristics of the data were explored by using clustering, thereby initializing GaMM parameters and so that a more precise characterization of data’s multimodality was obtained. Secondly, based on the framework of EM algorithm, a customized heuristic strategy was employed to address the challenge of parameter update difficulty caused by the absence of closed-updated expressions. The shape parameters of GaMM were updated by adopting this strategy towards maximizing the log-likelihood value gradually, while remaining parameters were updated in closed-form. A series of persuasive experiments were conducted to validate the feasibility, rationality, and effectiveness of the proposed Semi-EM algorithm. Experimental results demonstrate that the Semi-EM algorithm outperforms the four comparison algorithms in estimating multimodal probability distributions accurately. Specifically, the Semi-EM algorithm has lower error metrics and higher log-likelihood values, indicating that this algorithm can provide more accurate model parameter estimation and then obtain more precise representation of multimodal nature of the data.

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