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Lovasz theta function, SVMs and Finding Dense Subgraphs

Vinay Jethava (Institutionen för data- och informationsteknik, Datavetenskap (Chalmers)) ; Anders Martinsson (Institutionen för matematiska vetenskaper, matematisk statistik) ; C. Bhattacharyya ; Devdatt Dubhashi (Institutionen för data- och informationsteknik, Datavetenskap (Chalmers))
Journal of machine learning research (1532-4435). Vol. 14 (2013), p. 3495-3536.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: orthogonal labellings of graphs, planted cliques, random graphs, common dense subgraph



Denna post skapades 2014-06-23. Senast ändrad 2016-08-22.
CPL Pubid: 199483

 

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Institutioner (Chalmers)

Institutionen för data- och informationsteknik, Datavetenskap (Chalmers)
Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Data- och informationsvetenskap

Chalmers infrastruktur