{Behnam Roshanfekr Maryam Amirmazlaghani Saeed Saravani Zahra Dehghanian Alireza Amouzad}

Abstract

Graph embedding learning is a fundamental task when dealing with diverse datasets. While encoder–decoder architectures, such as U-Nets, have shown great success in image pixel-wise prediction tasks, applying similar methods to graph data poses challenges due to the lack of natural pooling and up-sampling operations for graphs. Recent methods leverage learnable parameters to extract structural information from neural networks and extend pooling and unpooling to graphs using node features and graph structural information. This paper proposes a novel model called GIUNet (Graph Isomorphism U-Net) for the graph classification task. The proposed Graph U-Net structure is based on graph isomorphism convolution while using a comprehensive pqPooling layer. The pqPooling layer in our approach effectively combines node features and graph structure information during the graph down-sampling stage. To incorporate graph structure information, we utilize both the spectral representation and node centrality measurements. Node centrality measurements capture various structural aspects of nodes in the graph, while the spectral representation helps us focus on the informative low-frequency components of the graph structure. Through ablation studies, we have demonstrated that leveraging the GIUNet model leads to significant improvements compared to state-of-the-art methods across multiple benchmark datasets.