Exploiting Optimization for Local Graph Clustering

TitleExploiting Optimization for Local Graph Clustering
Publication TypeMiscellaneous
Year of Publication2016
AuthorsFountoulakis, K., Chen X., Shun J., Roosta-Khorasani F., & Mahoney M. W.

Modern graph clustering applications require the analysis of large graphs which can be computationally expensive. In this regard, local spectral graph clustering methods aim to identify well-connected clusters around a given "seed set" of reference nodes without accessing the entire graph. This can be achieved, for example, by using the Approximate Personalized PageRank algorithm in the seminal paper by Andersen et al [1]. Here, we adopt an optimization perspective on this problem and draw connections between the local spectral algorithm of Andersen et al. [1] and an iterative shrinkage-thresholding algorithm. In particular, we show that, appropriately initialized ISTA can recover the sought-after local cluster in a time that only depends on the number of non-zeros of the optimal solution instead of the entire graph. In the process, we show that an optimization algorithm which apparently requires accessing the entire graph, can be made to behave completely local by accessing only a small number of nodes. This viewpoint builds a bridge across two seemingly disjoint fields of graph processing and numerical optimization, and allows one to leverage well-studied, numerically robust, and efficient optimization algorithms for processing today's large graphs.

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