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.

A mean field games approach to cluster analysis / Aquilanti, L.; Cacace, S.; Camilli, F.; De Maio, R.. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - 84:1(2021), pp. 299-323. [10.1007/s00245-019-09646-2]

### A mean field games approach to cluster analysis

#### 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.
##### Scheda breve Scheda completa
cluster analysis; expectation–maximization algorithm; mean field games; mixture model; multi-population model
01 Pubblicazione su rivista::01a Articolo in rivista
A mean field games approach to cluster analysis / Aquilanti, L.; Cacace, S.; Camilli, F.; De Maio, R.. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - 84:1(2021), pp. 299-323. [10.1007/s00245-019-09646-2]
File allegati a questo prodotto
File
Aquilanti_Mean_2020.pdf

accesso aperto

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/1401952`
• ND
• 0
• 1