The Spectral Zoo of Networks: Embedding and Visualizing Networks with Spectral Moments

Shengmin Jin, Reza Zafarani

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Network embedding methods have been widely and successfully used in network-based applications such as node classification and link prediction. However, an ideal network embedding should not only be useful for machine learning, but interpretable. We introduce a spectral embedding method for a network, its Spectral Point, which is basically the first few spectral moments of a network. Spectral moments are interpretable, where we prove their close relationships to network structure (e.g. number of triangles and squares) and various network properties (e.g. degree distribution, clustering coefficient, and network connectivity). Using spectral points, we introduce a visualizable and bounded 3D embedding space for all possible graphs, in which one can characterize various types of graphs (e.g., cycles), or real-world networks from different categories (e.g., social or biological networks). We demonstrate that spectral points can be used for network identification (i.e., what network is this subgraph sampled from?) and that by using just the first few moments one does not lose much predictive power.

Original languageEnglish (US)
Title of host publicationKDD 2020 - Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
PublisherAssociation for Computing Machinery
Pages1426-1434
Number of pages9
ISBN (Electronic)9781450379984
DOIs
StatePublished - Aug 23 2020
Event26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2020 - Virtual, Online, United States
Duration: Aug 23 2020Aug 27 2020

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Conference

Conference26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2020
Country/TerritoryUnited States
CityVirtual, Online
Period8/23/208/27/20

Keywords

  • graph spectrum
  • network embedding
  • network representation
  • network visualization
  • spectral graph theory

ASJC Scopus subject areas

  • Software
  • Information Systems

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