# Spectral Heterogeneous Graph Convolutions via Positive Noncommutative Polynomials

arXiv: https://arxiv.org/abs/2305.19872 · HTML: https://mlsanity.com/paper/2305.19872/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 30 of 39)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Heterogeneous Graph Transformer](https://mlsanity.com/paper/2003.01332/) (2020)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Are we really making much progress? Revisiting, benchmarking, and refining heterogeneous graph neural networks](https://mlsanity.com/paper/2112.14936/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [Self-supervised Heterogeneous Graph Neural Network with Co-contrastive Learning](https://mlsanity.com/paper/2105.09111/) (2021)
- [Representation Learning for Attributed Multiplex Heterogeneous Network](https://mlsanity.com/paper/1905.01669/) (2019)
- [Line Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2010.10046/) (2020)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Graph Attention Multi-Layer Perceptron](https://mlsanity.com/paper/2206.04355/) (2022)
- [Simple and Efficient Heterogeneous Graph Neural Network](https://mlsanity.com/paper/2207.02547/) (2022)
- [Graph Neural Networks Inspired by Classical Iterative Algorithms](https://mlsanity.com/paper/2103.06064/) (2021)
- [ASGN: An Active Semi-supervised Graph Neural Network for Molecular Property Prediction](https://mlsanity.com/paper/2007.03196/) (2020)

## Built on by (most cited first, 8 of 8)

- [Multi-Scale Heterogeneous Text-Attributed Graph Datasets From Diverse Domains](https://mlsanity.com/paper/2412.08937/) (2024)
- [Bootstrapping Heterogeneous Graph Representation Learning via Large Language Models: A Generalized Approach](https://mlsanity.com/paper/2412.08038/) (2024)
- [Loss-aware Curriculum Learning for Heterogeneous Graph Neural Networks](https://mlsanity.com/paper/2402.18875/) (2024)
- [Representation Learning with Mutual Influence of Modalities for Node Classification in Multi-Modal Heterogeneous Networks](https://mlsanity.com/paper/2505.07895/) (2025)
- [Chi-Square Wavelet Graph Neural Networks for Heterogeneous Graph Anomaly Detection](https://mlsanity.com/paper/2505.18934/) (2025)
- [Bridging RDF Knowledge Graphs with Graph Neural Networks for Semantically-Rich Recommender Systems](https://mlsanity.com/paper/2506.08743/) (2025)
- [Modality as Heterogeneity: Node Splitting and Graph Rewiring for Multimodal Graph Learning](https://mlsanity.com/paper/2602.00067/) (2026)
- [GCN-MPPR: Enhancing the Propagation of Message Passing Neural Networks via Motif-Based Personalized PageRank](https://mlsanity.com/paper/2602.07903/) (2026)

## Abstract (arXiv)

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.