关键词: 多模概率密度函数, Gamma混合模型, 期望最大化算法, 聚类, 对数似然函数

Abstract: The Expectation-Maximization (EM) algorithm plays an important role in parameter estimation for mixture models. However, existing EM algorithms for the Gamma Mixture Model (GaMM) have limitations. These limitations mainly arise from approximate computations leading to low-quality parameter estimates and inefficient computational performance due to numerical calculations. To address these limitations and fully exploit the multimodal nature of data, a Semi-EM algorithm was proposed to solve GaMM for multimodal probability distributions. Firstly, this algorithm used clustering to explore the spatial distribution characteristics of the data, allowing for an improved initialization of GaMM parameters and a more precise characterization of data’s multimodality. Secondly, based on the framework of the EM algorithm, a custom heuristic strategy was employed to address the challenge of parameter updates caused by the absence of closed-form expressions. The shape parameters of GaMM were gradually updated towards maximizing the log-likelihood value, while remaining parameters were updated in closed-form expressions. Finally, 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 four comparison algorithms in accurately estimating multimodal probability distributions. Specifically, the Semi-EM algorithm exhibits lower error metrics and higher log-likelihood values, indicating its ability to provide more accurate model parameter estimates and more precise characterization of the multimodal nature of the data.

Key words: multimodal probability density function, Gamma Mixture Model &#40, GaMM&#41, Expectation-Maximization &#40