A Mean Field Games approach to cluster analysis

Abstract: Cluster analysis is a classical problem in unsupervised Machine Learning which concerns the repartition of a group of  points into subgroups, in such a way that the elements within a same group are more similar to each other than they are to the elements of a different one. Most of the mathematical literature on cluster analysis, and more in general on Machine Learning, is in the framework of the finite-dimensional optimization.  In this talk, I will present  a multi-population Mean Field Games systems which can be interpreted as  an infinite-dimensional version of the classical Expectation-Maximization algorithm in soft clustering. I will discuss the theoretical aspects of the method and  the  application to some problems in cluster analysis.