LFGCN: Levitating over Graphs with Levy Flights

TL;DR

This paper introduces LFGCN, a novel graph convolutional network leveraging Levy flights for improved semi-supervised learning on graphs, especially heterogeneous ones, and proposes a new edge removal method to enhance training stability and accuracy.

Contribution

The paper presents a new LFGCN model incorporating Levy flights into graph convolutional networks and a P-DropEdge method based on Girvan-Newman for better graph topology learning.

Findings

LFGCN improves classification accuracy on semi-supervised tasks.

P-DropEdge accelerates training and enhances stability.

Case studies demonstrate utility in power grid analysis.

Abstract

Due to high utility in many applications, from social networks to blockchain to power grids, deep learning on non-Euclidean objects such as graphs and manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever increasing interest. We propose a new L\'evy Flights Graph Convolutional Networks (LFGCN) method for semi-supervised learning, which casts the L\'evy Flights into random walks on graphs and, as a result, allows both to accurately account for the intrinsic graph topology and to substantially improve classification performance, especially for heterogeneous graphs. Furthermore, we propose a new preferential P-DropEdge method based on the Girvan-Newman argument. That is, in contrast to uniform removing of edges as in DropEdge, following the Girvan-Newman algorithm, we detect network periphery structures using information on edge betweenness and then remove edges according to their betweenness centrality. Our experimental results on semi-supervised node classification tasks demonstrate that the LFGCN coupled with P-DropEdge accelerates the training task, increases stability and further improves predictive accuracy of learned graph topology structure. Finally, in our case studies we bring the machinery of LFGCN and other deep networks tools to analysis of power grid networks - the area where the utility of GDL remains untapped.