Mean field models for large data–clustering problems

Networks and Heterogeneous Media, vol. 15, pp. 463–487

Abstract

We consider mean-field models for data–clustering problems starting from a generalization of the bounded confidence model for opinion dynamics. The microscopic model includes information on the position as well as on additional features of the particles in order to develop specific clustering effects. The corresponding mean–field limit is derived and properties of the model are investigated analytically. In particular, the mean–field formulation allows the use of a random subsets algorithm for efficient computations of the clusters. Applications to shape detection and image segmentation on standard test images are presented and discussed.

Authors 3

1. Michaël Herty Aachen

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik -RWTH Aachen University -Templergraben 55, 52062 Aachen, Germany -

2. Lorenzo Pareschi corresponding

   University of Ferrara

   Affiliation as printed

   Mathematics and Computer Science Department -University of Ferrara -Via Machiavelli 35, 44121 Ferrara, Italy -

3. Giuseppe Visconti Aachen

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik -RWTH Aachen University -Templergraben 55, 52062 Aachen, Germany -