Learning Adaptive Multiresolution Transforms via Meta-Framelet-based Graph Convolutional Network

Graph Neural Networks are popular tools in graph representation learning that capture the graph structural properties. However, most GNNs employ single-resolution graph feature extraction, thereby failing to capture micro-level local patterns (high resolution) and macro-level graph cluster and community patterns (low resolution) simultaneously. Many multiresolution methods have been developed to capture graph patterns at multiple scales, but most of them depend on predefined and handcrafted multiresolution transforms that remain fixed throughout the training process once formulated. Due to variations in graph instances and distributions, fixed handcrafted transforms can not effectively tailor multiresolution representations to each graph instance. To acquire multiresolution representation suited to different graph instances and distributions, we introduce the Multiresolution Meta-Framelet-based Graph Convolutional Network (MM-FGCN), facilitating comprehensive and adaptive multiresolution analysis across diverse graphs. Extensive experiments demonstrate that our MM-FGCN achieves SOTA performance on various graph learning tasks.