  Graph neural networks (GNNs) have shown remarkable performance on homophilic
graph data while being far less impressive when handling non-homophilic graph
data due to the inherent low-pass filtering property of GNNs. In general, since
real-world graphs are often complex mixtures of diverse subgraph patterns,
learning a universal spectral filter on the graph from the global perspective
as in most current works may still suffer from great difficulty in adapting to
the variation of local patterns. On the basis of the theoretical analysis of
local patterns, we rethink the existing spectral filtering methods and propose
the node-oriented spectral filtering for graph neural network (namely NFGNN).
By estimating the node-oriented spectral filter for each node, NFGNN is
provided with the capability of precise local node positioning via the
generalized translated operator, thus discriminating the variations of local
homophily patterns adaptively. Meanwhile, the utilization of
re-parameterization brings a good trade-off between global consistency and
local sensibility for learning the node-oriented spectral filters. Furthermore,
we theoretically analyze the localization property of NFGNN, demonstrating that
the signal after adaptive filtering is still positioned around the
corresponding node. Extensive experimental results demonstrate that the
proposed NFGNN achieves more favorable performance.
