NDLI: Persistence-based clustering in riemannian manifolds

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Persistence-based clustering in riemannian manifolds

Content Provider	ACM Digital Library
Author	Chazal, Frédéric Skraba, Primoz Guibas, Leonidas J. Oudot, Steve Y.
Abstract	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 the size of the input distance matrix may be up to quadratic in the number of data points, a careful implementation only uses a linear amount of memory and takes barely more time to run than to read through the input. In this conference version of the paper we emphasize the experimental aspects of our work, describing the approach, giving an intuitive overview of its theoretical guarantees, discussing the choice of its parameters in practice, and demonstrating its potential in terms of applications through a series of experimental results obtained on synthetic and real-life data sets. Precise statements and proofs of our theoretical claims can be found in the full version of the paper [7].
Starting Page	97
Ending Page	106
Page Count	10
File Format	PDF
ISBN	9781450306829
DOI	10.1145/1998196.1998212
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-06-13
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Morse theory Topological persistence Mode seeking Clustering Unsupervised learning
Content Type	Text
Resource Type	Article

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