- Published 2015 in SDM

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 substructures 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 interest 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 structure 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.

Citations per Year

Averaging **20 citations** per year over the last 2 years.

@article{Benson2015TensorSC,
title={Tensor Spectral Clustering for Partitioning Higher-order Network Structures},
author={Austin R. Benson and David F. Gleich and Jure Leskovec},
journal={Proceedings of the ... SIAM International Conference on Data Mining. SIAM International Conference on Data Mining},
year={2015},
volume={2015},
pages={118-126}
}