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Diffusion-Convolutional Neural Networks

James Atwood, Don Towsley

TL;DR

This work introduces diffusion-convolutional neural networks (DCNNs), extending CNNs to graph-structured data by applying a diffusion-convolution operation that yields diffusion-based latent representations. The model uses a compact, ($O(HF)$) parameterization and is designed to be invariant to graph isomorphism, enabling efficient GPU-accelerated learning and prediction in polynomial time. Empirically, DCNNs achieve strong node classification performance on CORA and PubMed, and offer competitive results for graph classification across several datasets, though graph-level diffusion requires improved aggregation. The study also transparently discusses scalability limitations due to memory demands and locality constraints, and it situates DCNNs relative to PRMs and kernel methods, highlighting a distinct, differentiable, learnable diffusion-based approach.

Abstract

We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on the GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks.

Diffusion-Convolutional Neural Networks

TL;DR

This work introduces diffusion-convolutional neural networks (DCNNs), extending CNNs to graph-structured data by applying a diffusion-convolution operation that yields diffusion-based latent representations. The model uses a compact, () parameterization and is designed to be invariant to graph isomorphism, enabling efficient GPU-accelerated learning and prediction in polynomial time. Empirically, DCNNs achieve strong node classification performance on CORA and PubMed, and offer competitive results for graph classification across several datasets, though graph-level diffusion requires improved aggregation. The study also transparently discusses scalability limitations due to memory demands and locality constraints, and it situates DCNNs relative to PRMs and kernel methods, highlighting a distinct, differentiable, learnable diffusion-based approach.

Abstract

We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on the GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks.

Paper Structure

This paper contains 27 sections, 9 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Model
  3. Node Classification
  4. Graph Classification
  5. Edge Classification and Edge Features
  6. Purely Structural DCNNs
  7. Learning
  8. Experiments
  9. Node classification
  10. Protocol
  11. Baseline Methods
  12. Node Classification Data
  13. Results Discussion
  14. Graph Classification
  15. Protocol
  16. ...and 12 more sections

Figures (3)

  • Figure 1: DCNN model definition for node, graph, and edge classification tasks.
  • Figure 2: The effect of search breadth (\ref{['fig:nodesearchbreadth']}) and learning curves (\ref{['fig:nodeclasscoraprop']} - \ref{['fig:nodeclasspubmedprop']}) for the Cora and Pubmed datasets.
  • Figure 3: The effect of search breadth (\ref{['fig:graphclasssearch']}), as well as learning curves for the MUTAG (\ref{['fig:graphclassmutag']}) and ENZYMES (\ref{['fig:graphclassenzymes']}) datasets.