On Spectral Graph Embedding: A Non-Backtracking Perspective and Graph Approximation

TL;DR

This paper introduces NOBE, a spectral graph embedding framework based on non-backtracking walks, along with a graph approximation technique that preserves spectral properties, validated through experiments on real networks.

Contribution

The paper proposes a novel non-backtracking spectral embedding method and a graph approximation technique with theoretical guarantees, advancing graph analysis capabilities.

Findings

Effective clustering and structural hole detection demonstrated

Theoretical bounds on eigenvalue differences established

Method outperforms existing approaches on real-world networks

Abstract

Graph embedding has been proven to be efficient and effective in facilitating graph analysis. In this paper, we present a novel spectral framework called NOn-Backtracking Embedding (NOBE), which offers a new perspective that organizes graph data at a deep level by tracking the flow traversing on the edges with backtracking prohibited. Further, by analyzing the non-backtracking process, a technique called graph approximation is devised, which provides a channel to transform the spectral decomposition on an edge-to-edge matrix to that on a node-to-node matrix. Theoretical guarantees are provided by bounding the difference between the corresponding eigenvalues of the original graph and its graph approximation. Extensive experiments conducted on various real-world networks demonstrate the efficacy of our methods on both macroscopic and microscopic levels, including clustering and structural hole spanner detection.