FREDE: Linear-Space Anytime Graph Embeddings

• URL: http://arxiv.org/abs/2006.04746v1
• Date: Mon, 8 Jun 2020 16:51:24 GMT
• Title: FREDE: Linear-Space Anytime Graph Embeddings
• Authors: Anton Tsitsulin, Marina Munkhoeva, Davide Mottin, Panagiotis Karras, Ivan Oseledets, Emmanuel M\"uller
• Abstract summary: Low-dimensional representations, or embeddings, of a graph's nodes facilitate data mining tasks. FREquent Directions Embedding is a sketching-based method that iteratively improves on quality while processing rows of the similarity matrix individually. Our evaluation on variably sized networks shows that FREDE performs as well as SVD and competitively against current state-of-the-art methods in diverse data mining tasks.
• Score: 12.53022591889574
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Low-dimensional representations, or embeddings, of a graph's nodes facilitate data mining tasks. Known embedding methods explicitly or implicitly rely on a similarity measure among nodes. As the similarity matrix is quadratic, a tradeoff between space complexity and embedding quality arises; past research initially opted for heuristics and linear-transform factorizations, which allow for linear space but compromise on quality; recent research has proposed a quadratic-space solution as a viable option too. In this paper we observe that embedding methods effectively aim to preserve the covariance among the rows of a similarity matrix, and raise the question: is there a method that combines (i) linear space complexity, (ii) a nonlinear transform as its basis, and (iii) nontrivial quality guarantees? We answer this question in the affirmative, with FREDE(FREquent Directions Embedding), a sketching-based method that iteratively improves on quality while processing rows of the similarity matrix individually; thereby, it provides, at any iteration, column-covariance approximation guarantees that are, in due course, almost indistinguishable from those of the optimal row-covariance approximation by SVD. Our experimental evaluation on variably sized networks shows that FREDE performs as well as SVD and competitively against current state-of-the-art methods in diverse data mining tasks, even when it derives an embedding based on only 10% of node similarities.

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