A Mean Field Games approach to Cluster Analysis

2019/07/04 by Laura Aquilanti, Simone Cacace, Aquilanti, Laura +5 · 2 citations
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.AP #math.NA

paper · pdf · doi:10.48550/arxiv.1907.02261

arxiv created 2019/12/23 · arxiv updated 2019/12/24

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.

Cited by

• An Overview of Some Extensions of Mean Field Games beyond Perfect Homogeneity and Anonymity
• Monotone Multispecies Flows

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