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arXiv · 1907.02261

A Mean Field Games approach to Cluster Analysis

Laura Aquilanti·Simone Cacace·Fabio Camilli·Raul De Maio
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Abstract

In this paper, we develop a Mean Field Games approach to Cluster Analysis. We consider a finite mixture model, given by a convex combination of probability density functions, to describe the given data set. We interpret a data point as an agent of one of the populations represented by the components of the mixture model, and we introduce a corresponding optimal control problem. In this way, we obtain a multi-population Mean Field Games system which characterizes the parameters of the finite mixture model. Our method can be interpreted as a continuous version of the classical Expectation-Maximization algorithm.

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Laura Aquilanti, Simone Cacace, Fabio Camilli, Raul De Maio. 2019-07-04. A Mean Field Games approach to Cluster Analysis. https://arxiv.org/abs/1907.02261

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