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：从谱聚类到通过福克-普朗克插值的均值漂移

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: 在这项工作中，我们构建了一个统一的框架，以在基于密度和基于几何形状的数据聚类算法之间进行插值，并具体地将均值漂移算法与谱聚类在离散和连续水平上连接起来。 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的行为的新理论见解，并且在固定图上的扩散映射和均值漂移动力学之间提供了新的联系。 多个数值例子说明了我们的理论发现，并突出了在基于密度和基于几何形状的聚类算法之间进行插值的好处。