Graph Approximation and Clustering on a Budget

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Ethan Fetaya, Ohad Shamir, Shimon Ullman ;
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:241-249, 2015.

Abstract

We consider the problem of learning from a similarity matrix (such as spectral clustering and low-dimensional embedding), when computing pairwise similarities are costly, and only a limited number of entries can be observed. We provide a theoretical analysis using standard notions of graph approximation, significantly generalizing previous results, which focused on spectral clustering with two clusters. We also propose a new algorithmic approach based on adaptive sampling, which experimentally matches or improves on previous methods, while being considerably more general and computationally cheaper.

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