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Partitioning Well-Clustered Graphs: Spectral Clustering Works!

Authors
  • Peng, Richard
  • Sun, He
  • Zanetti, Luca
Type
Preprint
Publication Date
Nov 17, 2015
Submission Date
Nov 07, 2014
Identifiers
arXiv ID: 1411.2021
Source
arXiv
License
Yellow
External links

Abstract

In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and (2) grouping the embedded points into k clusters via k-means algorithms. We show that, for a wide class of graphs, spectral clustering gives a good approximation of the optimal clustering. While this approach was proposed in the early 1990s and has comprehensive applications, prior to our work similar results were known only for graphs generated from stochastic models. We also give a nearly-linear time algorithm for partitioning well-clustered graphs based on heat kernel embeddings and approximate nearest neighbor data structures.

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