A Mean Field Games Perspective on Evolutionary Clustering
Read the original on arXiv Statistics ML →The paper introduces a control‑theoretic framework for evolutionary clustering using quasi‑stationary Mean Field Games. Each cluster is modeled as a probability density whose dynamics follow a Fokker–Planck equation, while a stationary Hamilton–Jacobi equation determines the velocity field. In a Gaussian specialization, affine dynamics replicate the mean and covariance trajectories of the classical Expectation–Maximization algorithm, and the authors propose causal and non‑causal time‑averaged log‑likelihood objectives to enhance temporal coherence, along with a fully density‑based numerical implementation for non‑Gaussian components. The method is evaluated on synthetic and real time‑dependent datasets, compared to snapshot Expectation–Maximization, temporally smoothed observations, and an evolutionary k‑means baseline.
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