Cluster analysis consists of discovering set of patterns from a big data set. There are important applications in marketing, image processing, biology, medicine.
I will focus on soft-clustering, performed via finite mixture models, a probabilistic tool in the statistical analysis of data. In this setting, clusters are obtained as the results of an optimization problem through the implementation of the Expectation Maximization algorithm (EM). I will present a system of several coupled PDEs: a stationary multi-population Mean Field Games system, which can be considered as a continuous version of the EM algorithm. I will discuss the theoretical aspects of this method and show that the solution characterizes soft clusters within a big data set. Lastly, I will present some numerical results.
