A Mode-Partitioned Gamma Mixture Model Estimation Method for Large-Scale Multimodal Data

Gamma Mixture Model (GaMM) is a useful tool for representing complex distributions. However, estimating the parameters of GaMM faces challenges due to the lack of closed-form solution for the shape parameter. Existing parameter estimation methods face limitations stemming from their reliance on approximate computations, which degrade estimation accuracy, as well as the inherent complexity of numerical calculations, leading to computational inefficiency. To address these limitations and fully consider the multimodal nature of big data, this paper proposes a Mode-Partitioned GaMM (MP-GaMM) estimation method for large-scale multimodal data. The MP-GaMM method explores the spatial distribution characteristics of the data through clustering to partition the data into distinct modes, addresses mode overlap with a tune-up strategy, and employs closed-form estimator for parameter estimation of each mode in parallel. Experimental results demonstrate the rationality and effectiveness of the proposed MP-GaMM method, which outperforms existing methods in both accuracy and computational efficiency. Specifically, MP-GaMM exhibits lower error metrics, higher log-likelihood values and shorter runtime, indicating its capability to provide a more accurate estimation of the model parameters, and more precise characterization of the multimodal nature of large-scale data.