Statistical guarantees for local graph clustering release_6uunaxwjwrghnaepzwseztejoe

by Wooseok Ha and Kimon Fountoulakis and Michael W. Mahoney

Released as a article .

2019  

Abstract

Local graph clustering methods aim to find small clusters in very large graphs. These methods take as input a graph and a seed node, and they return as output a good cluster in a running time that depends on the size of the output cluster but that is independent of the size of the input graph. In this paper, we adopt a statistical perspective on local graph clustering, and we analyze the performance of the l1-regularized PageRank method~(Fountoulakis et. al.) for the recovery of a single target cluster, given a seed node inside the cluster. Assuming the target cluster has been generated by a random model, we present two results. In the first, we show that the optimal support of l1-regularized PageRank recovers the full target cluster, with bounded false positives. In the second, we show that if the seed node is connected solely to the target cluster then the optimal support of l1-regularized PageRank recovers exactly the target cluster. We also show empirically that l1-regularized PageRank has a state-of-the-art performance on many real graphs, demonstrating the superiority of the method. From a computational perspective, we show that the solution path of l1-regularized PageRank is monotonic. This allows for the application of the forward stagewise algorithm, which approximates the solution path in running time that does not depend on the size of the whole graph. Finally, we show that l1-regularized PageRank and approximate personalized PageRank (APPR), another very popular method for local graph clustering, are equivalent in the sense that we can lower and upper bound the output of one with the output of the other. Based on this relation, we establish for APPR similar results to those we establish for l1-regularized PageRank.
In text/plain format

Archived Files and Locations

application/pdf  1.2 MB
file_mjvozqnqdngsbmrxcmdwjzwp4u
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2019-06-11
Version   v1
Language   en ?
arXiv  1906.04863v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: ffc6eb06-31b9-4616-a224-c813a2b0df41
API URL: JSON