Layer-wise Adaptive Graph Convolution Networks Using Generalized Pagerank

TL;DR

This paper introduces AdaGPR, a novel adaptive layer-wise graph convolution method using generalized Pagerank, which improves accuracy and robustness in node classification tasks while providing interpretability of the convolution process.

Contribution

AdaGPR learns generalized Pageranks at each layer of GCNII, offering adaptive convolution, improved accuracy, robustness against oversmoothing, and interpretability of layer-wise convolution.

Findings

AdaGPR outperforms existing GCNs in accuracy on benchmark datasets.

AdaGPR demonstrates robustness against oversmoothing.

Layer-wise generalized Pagerank coefficients enable model interpretability.

Abstract

We investigate adaptive layer-wise graph convolution in deep GCN models. We propose AdaGPR to learn generalized Pageranks at each layer of a GCNII network to induce adaptive convolution. We show that the generalization bound for AdaGPR is bounded by a polynomial of the eigenvalue spectrum of the normalized adjacency matrix in the order of the number of generalized Pagerank coefficients. By analysing the generalization bounds we show that oversmoothing depends on both the convolutions by the higher orders of the normalized adjacency matrix and the depth of the model. We performed evaluations on node-classification using benchmark real data and show that AdaGPR provides improved accuracies compared to existing graph convolution networks while demonstrating robustness against oversmoothing. Further, we demonstrate that analysis of coefficients of layer-wise generalized Pageranks allows us to qualitatively understand convolution at each layer enabling model interpretations.