Journal article, 2013

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.

random graphs

common dense subgraph

orthogonal labellings of graphs

planted cliques

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Indian Institute of Science, Bangalore

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

1532-4435 (ISSN) 1533-7928 (eISSN)

Vol. 14 3495-3536Computer and Information Science