Faster Graph Embeddings via Coarsening

Matthew Fahrbach, Gramoz Goranci, Richard Peng, Sushant Sachdeva, Chi Wang
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:2953-2963, 2020.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-fahrbach20a, title = {Faster Graph Embeddings via Coarsening}, author = {Fahrbach, Matthew and Goranci, Gramoz and Peng, Richard and Sachdeva, Sushant and Wang, Chi}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {2953--2963}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/fahrbach20a/fahrbach20a.pdf}, url = {https://proceedings.mlr.press/v119/fahrbach20a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Faster Graph Embeddings via Coarsening %A Matthew Fahrbach %A Gramoz Goranci %A Richard Peng %A Sushant Sachdeva %A Chi Wang %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-fahrbach20a %I PMLR %P 2953--2963 %U https://proceedings.mlr.press/v119/fahrbach20a.html %V 119 %X 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.
APA
Fahrbach, M., Goranci, G., Peng, R., Sachdeva, S. & Wang, C.. (2020). Faster Graph Embeddings via Coarsening. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:2953-2963 Available from https://proceedings.mlr.press/v119/fahrbach20a.html.

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