Higher-Order Spectral Clustering for Geometric Graphs

Tensor Spectral Clustering for Partitioning Higher-order Network Structures

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) ...

General Tensor Spectral Co-clustering for Higher-Order Data

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral co-clustering method that simultaneously clusters the rows, columns, and slices of a nonnegative three-mode tensor and generalizes to tensors with any number of m...

Geometric and Higher Order Logicin

Spectral Co-Clustering for Dynamic Bipartite Graphs

A common task in many domains with a temporal aspect involves identifying and tracking clusters over time. Often dynamic data will have a feature-based representation. In some cases, a direct mapping will exist for both objects and features over time. But in many scenarios, smaller subsets of objects or features alone will persist across successive time periods. To address this issue, we propos...

Spectral clustering for multiclass Erdös-Rényi graphs

In this article, we study the properties of the spectral analysis of multiclass Erdös-Rényi graphs. With a view towards using the embedding afforded by the decomposition of the graph Laplacian for subsequent processing, we analyze two basic geometric properties, namely interclass intersection and interclass distance. We will first study the dyadic two-class case in details and observe the exist...