DMCA
Tensor Spectral Clustering for Partitioning Higher-order Network Structures
| Citations: | 2 - 1 self |
BibTeX
@MISC{Benson_tensorspectral,
author = {Austin R. Benson and et al.},
title = {Tensor Spectral Clustering for Partitioning Higher-order Network Structures},
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substruc-tures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of in-terest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order struc-ture of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.
Keyphrases
higher-order network structure tensor spectral clustering tsc algorithm feed-forward loop multilinear spectral method layered flow first-order markov chain important class standard spectral clustering algorithm important higher-order network substruc-tures directed 3-cycle di-rected 3-cycles large partition directed network random walk feedback loop particular interest higher-order struc-ture spectral graph theory-based method syn-thetic network spec-tral method graph anomaly detection
