Towards Better Graph Representation Learning with Parameterized
  Decomposition & Filtering
Mingqi Yang Wenjie Feng Yanming Shen Bryan Hooi
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.