Title: Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation Show Chinese title

Title: 图上的聚类动力学：通过福克-普朗克插值从谱聚类到均值漂移

Abstract: In this work we build a unifying framework to interpolate between density-driven and geometry-based algorithms for data clustering, and specifically, to connect the mean shift algorithm with spectral clustering at discrete and continuum levels. We seek this connection through the introduction of Fokker-Planck equations on data graphs. Besides introducing new forms of mean shift algorithms on graphs, we provide new theoretical insights on the behavior of the family of diffusion maps in the large sample limit as well as provide new connections between diffusion maps and mean shift dynamics on a fixed graph. Several numerical examples illustrate our theoretical findings and highlight the benefits of interpolating density-driven and geometry-based clustering algorithms. Show Chinese abstract

Abstract: 在本工作中，我们构建了一个统一的框架，在数据聚类中将密度驱动和基于几何的算法进行插值，并具体地在离散和连续层面上将均值漂移算法与谱聚类连接起来。 我们通过在数据图上引入福克-普朗克方程来寻求这种联系。 除了在图上引入新的均值漂移算法形式外，我们还提供了关于扩散映射族在大样本极限下行为的新理论见解，以及扩散映射与固定图上均值漂移动力学之间的新联系。 几个数值例子说明了我们的理论结果，并突出了在密度驱动和基于几何的聚类算法之间进行插值的优势。