arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.02817cs.LGcs.DSstat.ML
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通过粗化实现更快的图嵌入

Faster Graph Embeddings via Coarsening

Google Research(谷歌研究院);University of Toronto(多伦多大学);Georgia Institute of Technology(佐治亚理工学院);Microsoft Research(微软研究院)

Matthew Fahrbach, Gramoz Goranci, Richard Peng, Sushant Sachdeva, Chi Wang

AI总结:

针对大规模图中仅需少量相关顶点嵌入的问题,提出基于 Schur 补的图粗化方法及近线性时间算法,在保持预测精度的同时显著降低计算时间。

摘要:

图嵌入是在图结构数据上执行节点分类和链接预测等机器学习任务的常用工具。然而,即使我们只对一小部分相关顶点感兴趣,为大规模图计算嵌入的效率也低得令人难以接受。为解决这一问题,我们提出一种基于 Schur 补的高效图粗化方法,用于计算相关顶点的嵌入。我们证明,通过对非相关顶点进行 Gaussian 消元得到的 Schur 补图能够精确保留这些嵌入。由于计算 Schur 补代价高昂,我们给出一种近线性时间算法,用于在相关顶点上生成粗化图;该算法可证明在每次迭代中于期望意义下与 Schur 补相匹配。我们在图上预测任务中的实验表明,在粗化图而非整个图上计算嵌入,可显著节省时间,且不会牺牲准确性。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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