Rethinking the Graph Polynomial Filter via Positive and Negative
  Coupling Analysis
Haodong Wen Bodong Du Ruixun Liu Deyu Meng Xiangyong Cao
Recently, the optimization of polynomial filters within Spectral Graph Neural
Networks (GNNs) has emerged as a prominent research focus. Existing spectral
GNNs mainly emphasize polynomial properties in filter design, introducing
computational overhead and neglecting the integration of crucial graph
structure information. We argue that incorporating graph information into basis
construction can enhance understanding of polynomial basis, and further
facilitate simplified polynomial filter design. Motivated by this, we first
propose a Positive and Negative Coupling Analysis (PNCA) framework, where the
concepts of positive and negative activation are defined and their respective
and mixed effects are analysed. Then, we explore PNCA from the message
propagation perspective, revealing the subtle information hidden in the
activation process. Subsequently, PNCA is used to analyze the mainstream
polynomial filters, and a novel simple basis that decouples the positive and
negative activation and fully utilizes graph structure information is designed.
Finally, a simple GNN (called GSCNet) is proposed based on the new basis.
Experimental results on the benchmark datasets for node classification verify
that our GSCNet obtains better or comparable results compared with existing
state-of-the-art GNNs while demanding relatively less computational time.