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.