Spectral Heterogeneous Graph Convolutions via Positive Noncommutative Polynomials
This work addresses the problem of learning arbitrary valid heterogeneous graph filters with theoretical guarantees for researchers and practitioners in graph learning, representing a novel method for a known bottleneck rather than an incremental improvement.
The paper tackles the lack of theoretical guarantees and limited expressiveness in existing Heterogeneous Graph Neural Networks (HGNNs) by proposing PSHGCN, a Positive Spectral Heterogeneous Graph Convolutional Network, which outperforms all baselines on open benchmarks and efficiently scales to large real-world graphs with millions of nodes and edges.
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.