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.

中文翻译：

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大数据聚类问题的平均场模型

我们考虑用于数据聚类问题的均值模型，该模型从对意见动态的有界置信度模型的推广开始。微观模型包括有关粒子的位置以及其他特征的信息，以便产生特定的聚类效果。推导了相应的平均场极限，并对模型的性质进行了分析研究。特别是，均值场公式允许使用随机子集算法进行聚类的有效计算。提出并讨论了在标准测试图像上进行形状检测和图像分割的应用。