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Tensor Spectral Clustering for Partitioning Higher-order Network Structures.

Austin R Benson1, David F Gleich2, Jure Leskovec3

  • 1Institute for Computational and Mathematical Engineering, Stanford University. Supported by Stanford Graduate Fellowship.

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Summary
This summary is machine-generated.

Tensor Spectral Clustering (TSC) models higher-order network structures, outperforming standard methods in graph partitioning. This new approach effectively preserves complex network substructures like cycles and feedback loops.

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Area of Science:

  • Network Science
  • Graph Theory
  • Data Mining

Background:

  • Spectral methods analyze network structure via random walks but miss higher-order patterns like cycles.
  • Existing techniques are limited in capturing complex network substructures such as triangles and feedback loops.

Purpose of the Study:

  • Introduce a novel Tensor Spectral Clustering (TSC) algorithm for network partitioning.
  • Enable modeling and preservation of higher-order network structures within graph clustering.

Main Methods:

  • Represent higher-order network structures using tensors.
  • Develop a multilinear spectral method for tensor partitioning.
  • Apply the framework to layered flow discovery and graph anomaly detection.

Main Results:

  • TSC algorithm allows users to specify which higher-order structures to preserve during clustering.
  • Demonstrated effectiveness on synthetic networks for layered flow discovery and anomaly detection.
  • TSC significantly reduces the cutting of directed 3-cycles in directed networks compared to standard spectral clustering.

Conclusions:

  • Tensor Spectral Clustering offers a powerful framework for analyzing networks with complex higher-order structures.
  • The method enhances graph partitioning by incorporating information beyond first-order Markov chains.
  • TSC provides improved performance in tasks like feedback loop analysis and anomaly detection in directed networks.