Weighted Theta Functions and Embeddings with Applications to Max-Cut, Clustering and Summarization
Abstract
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.
Cite
Text
Johansson et al. "Weighted Theta Functions and Embeddings with Applications to Max-Cut, Clustering and Summarization." Neural Information Processing Systems, 2015.Markdown
[Johansson et al. "Weighted Theta Functions and Embeddings with Applications to Max-Cut, Clustering and Summarization." Neural Information Processing Systems, 2015.](https://mlanthology.org/neurips/2015/johansson2015neurips-weighted/)BibTeX
@inproceedings{johansson2015neurips-weighted,
title = {{Weighted Theta Functions and Embeddings with Applications to Max-Cut, Clustering and Summarization}},
author = {Johansson, Fredrik D and Chattoraj, Ankani and Bhattacharyya, Chiranjib and Dubhashi, Devdatt},
booktitle = {Neural Information Processing Systems},
year = {2015},
pages = {1018-1026},
url = {https://mlanthology.org/neurips/2015/johansson2015neurips-weighted/}
}