1,540 research outputs found
Consistency of spectral clustering in stochastic block models
We analyze the performance of spectral clustering for community extraction in
stochastic block models. We show that, under mild conditions, spectral
clustering applied to the adjacency matrix of the network can consistently
recover hidden communities even when the order of the maximum expected degree
is as small as , with the number of nodes. This result applies to
some popular polynomial time spectral clustering algorithms and is further
extended to degree corrected stochastic block models using a spherical
-median spectral clustering method. A key component of our analysis is a
combinatorial bound on the spectrum of binary random matrices, which is sharper
than the conventional matrix Bernstein inequality and may be of independent
interest.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1274 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Consistency of Spectral Hypergraph Partitioning under Planted Partition Model
Hypergraph partitioning lies at the heart of a number of problems in machine
learning and network sciences. Many algorithms for hypergraph partitioning have
been proposed that extend standard approaches for graph partitioning to the
case of hypergraphs. However, theoretical aspects of such methods have seldom
received attention in the literature as compared to the extensive studies on
the guarantees of graph partitioning. For instance, consistency results of
spectral graph partitioning under the stochastic block model are well known. In
this paper, we present a planted partition model for sparse random non-uniform
hypergraphs that generalizes the stochastic block model. We derive an error
bound for a spectral hypergraph partitioning algorithm under this model using
matrix concentration inequalities. To the best of our knowledge, this is the
first consistency result related to partitioning non-uniform hypergraphs.Comment: 35 pages, 2 figures, 1 tabl
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