A Generalization of Convolutional Neural Networks to Graph-Structured Data

TL;DR

This paper extends CNNs to graph-structured data using a novel spatial convolution based on random walks, enabling effective learning on non-grid data like molecules and images.

Contribution

It introduces a scalable, interpretable convolution method for graphs, broadening CNN applicability beyond grid data and demonstrating competitive results.

Findings

Effective on MNIST image data

Achieves state-of-the-art on molecular activity prediction

Scalable to large, varying graph structures

Abstract

This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations within the input, analogous to the way the standard convolution uses the spatial neighborhood of a pixel on the grid. The convolution has an intuitive interpretation, is efficient and scalable and can also be used on data with varying graph structure. Furthermore, this generalization can be applied to many standard regression or classification problems, by learning the the underlying graph. We empirically demonstrate the performance of the proposed CNN on MNIST, and challenge the state-of-the-art on Merck molecular activity data set.