Enhancing Gaussian Mixture Model Fitting via Equiprobable Binning and Adaptive Differential Evolution
摘要
Fitting Gaussian Mixture Models (GMMs) to one-dimensional data is a fundamental task in machine learning, traditionally addressed using the Expectation-Maximization (EM) algorithm. However, EM lacks inherent mechanisms to enforce separation between mixture components, a critical requirement in domains like medical research where distinct subgroups must be identified. Recently, the Distribution Optimization (DO) framework addressed this limitation by reformulating GMM estimation as a chi-squared goodness-of-fit minimization problem with an overlap penalty to enhance separation. However, its reliance on equiwidth binning and genetic algorithms can limit accuracy and scalability. In this paper, we refine the DO framework in two key ways: (1) replacing equiwidth binning with Mann–Wald’s equiprobable cells to improve estimation accuracy, and (2) adopting advanced Differential Evolution (DE) for more robust optimization of the high-dimensional parameter space. Through extensive experiments on synthetic and real-world datasets, we demonstrate that our refined approach significantly enhances accuracy, stability, and scalability compared to the original DO method.