On spectral graph embedding: A non-backtracking perspective and graph approximation

Abstract

Graph embedding has been proven to be efficient and effec-tive in facilitating graph analysis. In this paper, we present a novel spectral framework called NOn-Backtracking Embed-ding (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 analyz-ing the non-backtracking process, a technique called graph approximation is devised, which provides a channel to trans-form 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 cor-responding 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 clus-tering and structural hole spanner detection.