Mean field models for large data-clustering problems

Michael Herty, Lorenzo Pareschi and Giuseppe Visconti (preprint 8/9/2019 arXiv:1907.03585)

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.