A Linear Surrogate-Based Algorithm for Fitting Gaussian Mixture Functions

Gaussian Mixture Function (GMF) is a widely utilized model for analyzing and elucidating experimental data in science and engineering, where the fitting of GMF with noisy observations is usually rendered acomplicated nonlinear regression problem due to the underlying linear superposition of Gaussian components. Classical Newton-type solutions rely on derivatives of the regression objective to facilitate convergence, which are general-purpose and can be inefficient. In this letter, we propose a novel method inspiredby Majorization-Minimization (MM) to achieve efficient GMF fitting in a linear manner. The proposed method integrates the contribution of each Gaussian component in GMF to construct a linear surrogate and ensures the consistent convergence of the original nonlinear objective. Extensive experiments demonstrate that the proposed method outperforms classical solutions in convergence speed while maintaining precise fitting accuracy.