Weighted theta functions and embeddings with applications to Max-Cut, clustering and summarization
Conference contribution, 2015

We introduce a unifying generalization of the Lovász theta function, and the associated geometric embedding, for graphs with weights on both nodes and edges. We show how it can be computed exactly by semidefinite programming, and how to approximate it using SVM computations. We show how the theta function can be interpreted as a measure of diversity in graphs and use this idea, and the graph embedding in algorithms for Max-Cut, correlation clustering and document summarization, all of which are well represented as problems on weighted graphs.

Semi-definite programming

Geometric embedding


Document summarization

Graph embeddings

Weighted graph


Correlation clustering

Information science


Fredrik Johansson

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

A. Chattoraj

Chalmers University of Technology

University of Rochester

C. Bhattacharyya

Indian Institute of Science, Bangalore

Devdatt Dubhashi

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

29th Annual Conference on Neural Information Processing Systems, NIPS 2015, Montreal, Canada, 7-12 December

1049-5258 (ISSN)

Vol. 2015-January 1018-1026

Subject Categories

Discrete Mathematics