  Heterogeneous Graph Neural Networks (HGNNs) have gained significant
popularity in various heterogeneous graph learning tasks. However, most
existing HGNNs rely on spatial domain-based methods to aggregate information,
i.e., manually selected meta-paths or some heuristic modules, lacking
theoretical guarantees. Furthermore, these methods cannot learn arbitrary valid
heterogeneous graph filters within the spectral domain, which have limited
expressiveness. To tackle these issues, we present a positive spectral
heterogeneous graph convolution via positive noncommutative polynomials. Then,
using this convolution, we propose PSHGCN, a novel Positive Spectral
Heterogeneous Graph Convolutional Network. PSHGCN offers a simple yet effective
method for learning valid heterogeneous graph filters. Moreover, we demonstrate
the rationale of PSHGCN in the graph optimization framework. We conducted an
extensive experimental study to show that PSHGCN can learn diverse
heterogeneous graph filters and outperform all baselines on open benchmarks.
Notably, PSHGCN exhibits remarkable scalability, efficiently handling large
real-world graphs comprising millions of nodes and edges. Our codes are
available at https://github.com/ivam-he/PSHGCN.
