Publication 21-CNA-018

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

Katy Craig
Department of Mathematics
University of California
Santa Barbara, CA 93117, USA
kcraig@math.ucsb.edu

Nicolas García Trillos
Department of Statistics
University of Wisconsin Madison
1300 University Avenue Madison, WI 53706
garciatrillo@wisc.edu

Dejan Slepčev
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
slepcev@andrew.cmu.edu

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.

Get the paper in its entirety as  21-CNA-018.pdf

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