A Mean Field Games approach to Cluster Analysis
Numerical Analysis
2019-12-24 v2 Numerical Analysis
Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1907.02261,
title = {A Mean Field Games approach to Cluster Analysis},
author = {Laura Aquilanti and Simone Cacace and Fabio Camilli and Raul De Maio},
journal= {arXiv preprint arXiv:1907.02261},
year = {2019}
}