FREDE：随时图形嵌入
FREDE: Anytime Graph Embeddings
摘要：
图的节点的低维表示或嵌入促进了几个实际的数据科学和数据工程任务。由于这种嵌入显式或隐式地依赖于节点之间的相似性度量，因此它们需要计算二次相似性矩阵，从而在空间复杂度和嵌入质量之间进行权衡。迄今为止，没有图嵌入工作结合（i）线性空间复杂度，（ii）作为其基础的非线性变换，（iii）非平凡的质量保证。在本文中，我们介绍FREDE（FREquent方向嵌入），一个图形嵌入的基础上矩阵素描，结合这三个desiderata。从嵌入方法旨在保持相似性矩阵的行之间的协方差的观察出发，FREDE迭代地改进质量，同时单独处理从现有技术的图嵌入方法导出的非线性变换的PPR相似性矩阵的行，并且在任何迭代处提供，列协方差近似保证在适当的时候几乎没有区别的SVD的最佳近似。我们对大型网络的实验评估表明，FREDE的性能几乎与SVD一样好，并且在各种数据科学任务中与最先进的嵌入方法竞争，即使它基于低至10%的节点相似性。
英文摘要：
Low-dimensional representations, or embeddings, of a graph's nodes facilitate several practical data science and data engineering tasks. As such embeddings rely, explicitly or implicitly, on a similarity measure among nodes, they require the computation of a quadratic similarity matrix, inducing a tradeoff between space complexity and embedding quality. To date, no graph embedding work combines (i) linear space complexity, (ii) a nonlinear transform as its basis, and (iii) nontrivial quality guarantees. In this paper we introduce FREDE (FREquent Directions Embedding), a graph embedding based on matrix sketching that combines those three desiderata. Starting out from the observation that embedding methods aim to preserve the covariance among the rows of a similarity matrix}, FREDE iteratively improves on quality while individually processing rows of a nonlinearly transformed PPR similarity matrix derived from a state-of-the-art graph embedding method} and provides, at any iteration, column-covariance approximation guarantees in due course almost indistinguishable from those of the optimal approximation by SVD. Our experimental evaluation on variably sized networks shows that FREDE performs almost as well as SVD and competitively against state-of-the-art embedding methods in diverse data science tasks, even when it is based on as little as 10% of node similarities.
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