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Faster Graph Embeddings via Coarsening
Matthew Fahrbach · Gramoz Goranci · Richard Peng · Sushant Sachdeva · Chi Wang

Tue Jul 14 07:00 AM -- 07:45 AM & Tue Jul 14 06:00 PM -- 06:45 PM (PDT) @ None #None

Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we are interested only in a small subset of relevant vertices. To address this, we present an efficient graph coarsening approach, based on Schur complements, for computing the embedding of the relevant vertices. We prove that these embeddings are preserved exactly by the Schur complement graph that is obtained via Gaussian elimination on the non-relevant vertices. As computing Schur complements is expensive, we give a nearly-linear time algorithm that generates a coarsened graph on the relevant vertices that provably matches the Schur complement in expectation in each iteration. Our experiments involving prediction tasks on graphs demonstrate that computing embeddings on the coarsened graph, rather than the entire graph, leads to significant time savings without sacrificing accuracy.

Author Information

Matthew Fahrbach (Georgia Institute of Technology)
Gramoz Goranci (University of Toronto)
Richard Peng (Georgia Tech / MSR Redmond)
Sushant Sachdeva (University of Toronto)
Chi Wang (Microsoft Research)

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