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A Scalable Unsupervised Framework for Comparing Graph Embeddings

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 12091)

Abstract

Graph embedding is a transformation of vertices of a graph into a set of vectors. A good embedding should capture the graph topology, vertex-to-vertex relationship, and other relevant information about the graph, its subgraphs, and vertices. If these objectives are achieved, an embedding is a meaningful, understandable, and often compressed representations of a network. Unfortunately, selecting the best embedding is a challenging task and very often requires domain experts.

In the recent paper [1], we propose a “divergence score” that can be assigned to embeddings to help distinguish good ones from bad ones. This general framework provides a tool for an unsupervised graph embedding comparison. The complexity of the original algorithm was quadratic in the number of vertices. It was enough to show that the proposed method is feasible and has practical potential (proof-of-concept). In this paper, we improve the complexity of the original framework and design a scalable approximation algorithm. Moreover, we perform some detailed quality and speed benchmarks.

Keywords

Graph embedding Geometric Chung-Lu Model 

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Copyright information

© Crown 2020

Authors and Affiliations

  1. 1.Decision Analysis and Support Unit, SGH Warsaw School of EconomicsWarsawPoland
  2. 2.Department of MathematicsRyerson UniversityTorontoCanada
  3. 3.Tutte Institute for Mathematics and ComputingOttawaCanada

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