Graph Neural Networks with Haar Transform-Based Convolution and Pooling: A Complete Guide

Graph Neural Networks (GNNs) have recently caught great attention and achieved significant progress in graph-level applications. In order to handle graphs with different features and sizes, we propose a novel graph neural network, which we call HaarNet, to predict graph labels with interrelated convolution and pooling strategies. Similar to some existing routines, the model assembles unified graph-level representations from samples by first adopting graph convolutional layers to extract mutual information followed by graph pooling layers to downsample graph resolution. By a sequence of clusterings, we embed the intrinsic topological information of each graph into the GNN. Through the fast Haar transformation, we made our contribution to forming a smooth workflow that learns multi-scale graph representation with redundancy removed. As a result, our proposed framework obtains notable accuracy gains without sacrificing performance stability. Extensive experiments validate the superiority on graph classification and regression tasks, where our proposed HaarNet outperforms various existing GNN models, especially on big data sets.