Towards Better Graph Representation Learning with Parameterized Decomposition & Filtering
This work addresses the problem of enhancing flexibility and mitigating issues like smoothness in graph neural networks for researchers and practitioners in graph learning, representing an incremental advancement.
The authors tackled the challenge of effective graph representation by proposing a novel framework that unifies existing GNN models through parameterized decomposition and filtering, achieving significant improvements and computational efficiency across various graph learning tasks.
Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.