Walk-Steered Convolution for Graph Classification

TL;DR

This paper introduces a walk-steered convolutional network that uses random walk paths and Gaussian modeling to effectively capture subgraph structures for improved graph classification performance.

Contribution

It proposes a novel walk-steered convolutional approach with multi-scale walk fields and Gaussian encoding, enhancing scalability and representation of graph data.

Findings

Outperforms state-of-the-art methods on multiple graph classification datasets.

Utilizes Gaussian mixture models to encode walk path variations.

Incorporates graph coarsening for high-level semantic learning.

Abstract

Graph classification is a fundamental but challenging issue for numerous real-world applications. Despite recent great progress in image/video classification, convolutional neural networks (CNNs) cannot yet cater to graphs well because of graphical non-Euclidean topology. In this work, we propose a walk-steered convolutional (WSC) network to assemble the essential success of standard convolutional neural networks as well as the powerful representation ability of random walk. Instead of deterministic neighbor searching used in previous graphical CNNs, we construct multi-scale walk fields (a.k.a. local receptive fields) with random walk paths to depict subgraph structures and advocate graph scalability. To express the internal variations of a walk field, Gaussian mixture models are introduced to encode principal components of walk paths therein. As an analogy to a standard convolution kernel on image, Gaussian models implicitly coordinate those unordered vertices/nodes and edges in a local receptive field after projecting to the gradient space of Gaussian parameters. We further stack graph coarsening upon Gaussian encoding by using dynamic clustering, such that high-level semantics of graph can be well learned like the conventional pooling on image. The experimental results on several public datasets demonstrate the superiority of our proposed WSC method over many state-of-the-arts for graph classification.