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Lovasz theta function, SVMs and Finding Dense Subgraphs

Jethava, Vinay and Martinsson, Anders and Bhattacharyya, Chiranjib and Dubhashi, Devdatt (2013) Lovasz theta function, SVMs and Finding Dense Subgraphs. In: JOURNAL OF MACHINE LEARNING RESEARCH, 14 . pp. 3495-3536.

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Abstract

In this paper we establish that the Lovasz theta function on a graph can be restated as a kernel learning problem. We introduce the notion of SVM-theta graphs, on which Lovasz theta function can be approximated well by a Support vector machine (SVM). We show that Erdos-Renyi random G(n, p) graphs are SVM-theta graphs for log(4)n/n <= p < 1. Even if we embed a large clique of size Theta(root np/1-p) in a G(n, p) graph the resultant graph still remains a SVM-theta graph. This immediately suggests an SVM based algorithm for recovering a large planted clique in random graphs. Associated with the theta function is the notion of orthogonal labellings. We introduce common orthogonal labellings which extends the idea of orthogonal labellings to multiple graphs. This allows us to propose a Multiple Kernel learning (MKL) based solution which is capable of identifying a large common dense subgraph in multiple graphs. Both in the planted clique case and common subgraph detection problem the proposed solutions beat the state of the art by an order of magnitude.

Item Type: Journal Article
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Additional Information: copyright for this article belongs to MICROTOME PUBL, 31 GIBBS ST, BROOKLINE, MA 02446 USA
Keywords: orthogonal labellings of graphs; planted cliques; random graphs; common dense subgraph
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 10 Jun 2014 05:21
Last Modified: 10 Jun 2014 05:21
URI: http://eprints.iisc.ernet.in/id/eprint/49201

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