Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation
This work provides a theoretical bridge between clustering methods, which is incremental for researchers in machine learning and data analysis.
The authors tackled the problem of connecting density-driven and geometry-based clustering algorithms by introducing a unifying framework using Fokker-Planck equations on graphs, resulting in new forms of mean shift algorithms and theoretical insights into diffusion maps.
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.