Graph Polynomial Convolution Models for Node Classification of Non-Homophilous Graphs

TL;DR

This paper introduces novel graph polynomial convolution models for node classification on non-homophilous graphs, combining higher-order convolution and adaptive learning to improve accuracy and generalization.

Contribution

It proposes new polynomial-based graph convolution models with adaptive scaling, offering theoretical bounds and improved empirical performance on non-homophilous graphs.

Findings

Improved node classification accuracy on non-homophilous graphs.

Theoretical generalization bounds depend on eigenvalue spectrum and scaling parameters.

Adaptive models outperform fixed-parameter models in experiments.

Abstract

We investigate efficient learning from higher-order graph convolution and learning directly from adjacency matrices for node classification. We revisit the scaled graph residual network and remove ReLU activation from residual layers and apply a single weight matrix at each residual layer. We show that the resulting model lead to new graph convolution models as a polynomial of the normalized adjacency matrix, the residual weight matrix, and the residual scaling parameter. Additionally, we propose adaptive learning between directly graph polynomial convolution models and learning directly from the adjacency matrix. Furthermore, we propose fully adaptive models to learn scaling parameters at each residual layer. We show that generalization bounds of proposed methods are bounded as a polynomial of eigenvalue spectrum, scaling parameters, and upper bounds of residual weights. By theoretical analysis, we argue that the proposed models can obtain improved generalization bounds by limiting the higher-orders of convolutions and direct learning from the adjacency matrix. Using a wide set of real-data, we demonstrate that the proposed methods obtain improved accuracy for node-classification of non-homophilous graphs.