A Multi-Frequency Information Graph Representation for Graph Classification

This paper proposes a novel graph classification method to tackle the categorization of complex and irregularly structured graphs, demonstrating state-of-the-art performance on several benchmarks. This method is predicated on the principle of graph signal decomposition. Although significant research has been conducted on frequency decomposition for node classification tasks, its application to graph classification has not been extensively explored. To this end, we introduce an innovative graph classification framework known as the Multi-Frequency Graph Convolutional Network (MFGCN). The MFGCN framework operates by capturing both high-frequency and low-frequency information within graph data at various hierarchical levels, thereby enriching the graph representation, which is crucial for classification tasks. Subsequently, these multi-frequency graph representations are processed using 3D convolutional layers, followed by fully connected layers to perform the classification. We have conducted a theoretical analysis on the extraction of high and low-frequency signals from graph signals. To validate the efficiency of our MFGCN framework, we evaluated it against six benchmark datasets: COLLAB, MUTAG, IMDB-BINARY, PROTEINS, IMDB-MULTI, and D&D. Our results demonstrate a marked improvement in graph classification accuracy when compared to the most advanced existing methods.