# HAQJSK: Hierarchical-Aligned Quantum Jensen-Shannon Kernels for Graph Classification

arXiv: https://arxiv.org/abs/2211.02904 · HTML: https://mlsanity.com/paper/2211.02904/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 70 references that are in the map.
- First posted on arXiv 5 Nov 2022.

## Builds on (most cited first, 9 of 9)

- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Graph Kernels: State-of-the-Art and Future Challenges](https://mlsanity.com/paper/2011.03854/) (2020)
- [Anonymous Walk Embeddings](https://mlsanity.com/paper/1805.11921/) (2018)
- [Graph Filtration Kernels](https://mlsanity.com/paper/2110.11862/) (2021)
- [The Weight Function in the Subtree Kernel is Decisive](https://mlsanity.com/paper/1904.05421/) (2019)
- [Tree++: Truncated Tree Based Graph Kernels](https://mlsanity.com/paper/2002.09846/) (2020)

## Built on by (most cited first, 18 of 18)

- [SpeGCL: Self-supervised Graph Spectrum Contrastive Learning without Positive Samples](https://mlsanity.com/paper/2410.10365/) (2024)
- [Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approach](https://mlsanity.com/paper/2506.13083/) (2025)
- [On the Probability of Necessity and Sufficiency of Explaining Graph Neural Networks: A Lower Bound Optimization Approach](https://mlsanity.com/paper/2212.07056/) (2022)
- [Topology-aware Reinforcement Feature Space Reconstruction for Graph Data](https://mlsanity.com/paper/2411.05742/) (2024)
- [DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networks](https://mlsanity.com/paper/2310.02027/) (2023)
- [SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classification](https://mlsanity.com/paper/2408.16698/) (2024)
- [QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning](https://mlsanity.com/paper/2504.11083/) (2025)
- [Convolutional and Deep Learning based techniques for Time Series Ordinal Classification](https://mlsanity.com/paper/2306.10084/) (2023)
- [Derivation of Back-propagation for Graph Convolutional Networks using Matrix Calculus and its Application to Explainable Artificial Intelligence](https://mlsanity.com/paper/2408.01408/) (2024)
- [MALADY: Multiclass Active Learning with Auction Dynamics on Graphs](https://mlsanity.com/paper/2409.09475/) (2024)
- [Decorrelation-based Self-Supervised Visual Representation Learning for Writer Identification](https://mlsanity.com/paper/2410.01441/) (2024)
- [Graph Signal Adaptive Message Passing](https://mlsanity.com/paper/2410.17629/) (2024)
- [AKBR: Learning Adaptive Kernel-based Representations for Graph Classification](https://mlsanity.com/paper/2403.16130/) (2024)
- [Mitigating Degree Bias in Graph Representation Learning with Learnable Structural Augmentation and Structural Self-Attention](https://mlsanity.com/paper/2504.15075/) (2025)
- [Directed Link Prediction using GNN with Local and Global Feature Fusion](https://mlsanity.com/paper/2506.20235/) (2025)
- [CTQWformer: A CTQW-based Transformer for Graph Classification](https://mlsanity.com/paper/2605.09486/) (2026)
- [Cross-Domain Molecular Relational Learning: Leveraging Chemical Structure-Activity Analysis](https://mlsanity.com/paper/2605.16799/) (2026)
- [TGFormer: Towards Temporal Graph Transformer with Auto-Correlation Mechanism](https://mlsanity.com/paper/2605.24971/) (2026)

## Abstract (arXiv)

In this work, we propose a family of novel quantum kernels, namely the Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed graphs. Different from most existing classical graph kernels, the proposed HAQJSK kernels can incorporate hierarchical aligned structure information between graphs and transform graphs of random sizes into fixed-sized aligned graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of vertices and the Hierarchical Transitive Aligned Density Matrix of the Continuous-Time Quantum Walk (CTQW). For a pair of graphs to hand, the resulting HAQJSK kernels are defined by measuring the Quantum Jensen-Shannon Divergence (QJSD) between their transitive aligned graph structures. We show that the proposed HAQJSK kernels not only reflect richer intrinsic global graph characteristics in terms of the CTQW, but also address the drawback of neglecting structural correspondence information arising in most existing R-convolution kernels. Furthermore, unlike the previous Quantum Jensen-Shannon Kernels associated with the QJSD and the CTQW, the proposed HAQJSK kernels can simultaneously guarantee the properties of permutation invariant and positive definiteness, explaining the theoretical advantages of the HAQJSK kernels. Experiments indicate the effectiveness of the proposed kernels.