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.
Aquilanti, L., Cacace, S., Camilli, F., De Maio, R. (2020). A Mean Field Games Approach to Cluster Analysis. APPLIED MATHEMATICS AND OPTIMIZATION [10.1007/s00245-019-09646-2].