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 a complicated 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 inspired by 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.