# Mean field models for large data-clustering problems

## TL;DR

This paper develops mean-field models for data clustering, extending opinion dynamics models to include particle features, enabling efficient clustering algorithms with applications in shape detection and image segmentation.

## Contribution

It introduces a novel mean-field approach for clustering that incorporates particle features and derives an efficient algorithm for practical applications.

## Key findings

- Mean-field models effectively capture clustering behavior.
- The approach enables efficient computation of clusters.
- Applications demonstrate improved shape detection and segmentation.

## 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.