Evolving Gaussian Mixture Models with Splitting and Merging Mutation Operators.

Area of Science:

• Machine Learning
• Computational Statistics
• Evolutionary Computation

Background:

• Gaussian mixture models (GMMs) are widely used for density estimation and clustering.
• Traditional Expectation Maximization (EM) algorithms can be sensitive to initialization and may converge to local optima.
• Existing advanced methods like genetic-based EM (GA-EM) offer improvements but can be parameter-dependent.

Purpose of the Study:

• To introduce and analyze the Evolutionary Split and Merge for Expectation Maximization (ESM-EM) algorithm and its variants.
• To evaluate the computational efficiency and performance of ESM-EM compared to standard EM and GA-EM.
• To develop a parameter-free variant of ESM-EM.

Main Methods:

• Development of the ESM-EM algorithm utilizing split and merge operations to evolve GMMs.
• Asymptotic time complexity analysis to compare ESM-EM with GA-EM.
• Empirical evaluation on 35 diverse datasets.
• Comparison with multiple runs of standard EM and a parameter-free ESM-EM variant against fine-tuned GA-EM.

Main Results:

• ESM-EM algorithms exhibit competitive asymptotic time complexity compared to GA-EM.
• ESM-EM demonstrates significant computational efficiency over multiple runs of standard EM.
• A parameter-free ESM-EM variant achieves results comparable to a fine-tuned GA-EM algorithm.

Conclusions:

• ESM-EM provides an efficient and competitive approach for evolving Gaussian mixture models.
• The parameter-free variant offers a robust alternative to GA-EM, reducing the need for extensive parameter tuning.
• ESM-EM represents a valuable advancement in model-based clustering and density estimation.