# A Mean Field Games approach to Cluster Analysis

## TL;DR

This paper introduces a novel Mean Field Games framework for cluster analysis, modeling data points as agents in a multi-population system to estimate mixture model parameters, offering a continuous alternative to the EM algorithm.

## Contribution

It develops a new Mean Field Games approach for finite mixture models, providing a continuous, game-theoretic perspective on clustering.

## Key findings

- Formulates a multi-population MFG system for parameter estimation
- Provides a continuous analog to the Expectation-Maximization algorithm
- Demonstrates the effectiveness of the approach on clustering tasks

## 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.