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

We investigate graph convolution networks with efficient learning from higher-order graph convolutions and direct learning 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 models lead to new graph polynomial convolution methods constructed as polynomials of the normalized adjacency matrix, the residual weight matrix, and the residual scaling parameter. Additionally, we propose adaptive learning between graph polynomial convolution models and direct learning from the adjacency matrix. Furthermore, we propose fully adaptive models that 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,