Persistence-based clustering in riemannian manifolds

We present a clustering scheme that combines a mode-seeking phase with a cluster merging phase in the corresponding density map. While mode detection is done by a standard graph-based hill-climbing scheme, the novelty of our approach resides in its use of topological persistence to guide the merging of clusters. Our algorithm provides additional feedback in the form of a set of points in the plane, called a persistence diagram (PD), which provably reflects the prominences of the modes of the density. In practice, this feedback enables the user to choose relevant parameter values, so that under mild sampling conditions the algorithm will output the correct number of clusters, a notion that can be made formally sound within persistence theory. The algorithm only requires rough estimates of the density at the data points, and knowledge of (approximate) pairwise distances between them. It is therefore applicable in any metric space. Meanwhile, its complexity remains practical: although t...

• Type: Journal
• Year: 2011
• Where: COMPGEOM
• Authors: Frédéric Chazal, Leonidas J. Guibas, Steve Y. Oudot, Primoz Skraba
• Keywords: Analysis Of Algorithms, COMPGEOM 2011, Discrete Geometry, Pairwise Distances, Problem Complexity