Graph Approximation and Clustering on a Budget

TL;DR

This paper addresses the challenge of learning from similarity matrices with costly pairwise computations by proposing a theoretical framework for graph approximation and an adaptive sampling algorithm that improves efficiency.

Contribution

It introduces a generalized theoretical analysis for graph approximation and a novel adaptive sampling algorithm that is more efficient and broadly applicable.

Findings

Theoretical analysis significantly generalizes previous results.

The proposed algorithm matches or outperforms existing methods.

Algorithm is computationally cheaper and more versatile.

Abstract

We consider the problem of learning from a similarity matrix (such as spectral clustering and lowd imensional 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.