# Disentangled Graph Representation Based on Substructure-Aware Graph Optimal Matching Kernel Convolutional Networks

arXiv: https://arxiv.org/abs/2504.16360 · HTML: https://mlsanity.com/paper/2504.16360/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2012.09641/) (2020)
- [Network Representation Learning: A Survey](https://mlsanity.com/paper/1801.05852/) (2017)
- [Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure](https://mlsanity.com/paper/2209.14107/) (2022)
- [Factorizable Graph Convolutional Networks](https://mlsanity.com/paper/2010.05421/) (2020)
- [KerGNNs: Interpretable Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/2201.00491/) (2022)
- [On Valid Optimal Assignment Kernels and Applications to Graph Classification](https://mlsanity.com/paper/1606.01141/) (2016)
- [Independence Promoted Graph Disentangled Networks](https://mlsanity.com/paper/1911.11430/) (2019)
- [RetGK: Graph Kernels based on Return Probabilities of Random Walks](https://mlsanity.com/paper/1809.02670/) (2018)
- [The Expressive Power of Graph Neural Networks: A Survey](https://mlsanity.com/paper/2308.08235/) (2023)
- [Interpretable Deep Graph Generation with Node-Edge Co-Disentanglement](https://mlsanity.com/paper/2006.05385/) (2020)
- [Drug Similarity Integration Through Attentive Multi-view Graph Auto-Encoders](https://mlsanity.com/paper/1804.10850/) (2018)
- [Motif Graph Neural Network](https://mlsanity.com/paper/2112.14900/) (2021)
- [Descriptive Kernel Convolution Network with Improved Random Walk Kernel](https://mlsanity.com/paper/2402.06087/) (2024)
- [LGD-GCN: Local and Global Disentangled Graph Convolutional Networks](https://mlsanity.com/paper/2104.11893/) (2021)

## Abstract (arXiv)

Graphs effectively characterize relational data, driving graph representation learning methods that uncover underlying predictive information. As state-of-the-art approaches, Graph Neural Networks (GNNs) enable end-to-end learning for diverse tasks. Recent disentangled graph representation learning enhances interpretability by decoupling independent factors in graph data. However, existing methods often implicitly and coarsely characterize graph structures, limiting structural pattern analysis within the graph. This paper proposes the Graph Optimal Matching Kernel Convolutional Network (GOMKCN) to address this limitation. We view graphs as node-centric subgraphs, where each subgraph acts as a structural factor encoding position-specific information. This transforms graph prediction into structural pattern recognition. Inspired by CNNs, GOMKCN introduces the Graph Optimal Matching Kernel (GOMK) as a convolutional operator, computing similarities between subgraphs and learnable graph filters. Mathematically, GOMK maps subgraphs and filters into a Hilbert space, representing graphs as point sets. Disentangled representations emerge from projecting subgraphs onto task-optimized filters, which adaptively capture relevant structural patterns via gradient descent. Crucially, GOMK incorporates local correspondences in similarity measurement, resolving the trade-off between differentiability and accuracy in graph kernels. Experiments validate that GOMKCN achieves superior accuracy and interpretability in graph pattern mining and prediction. The framework advances the theoretical foundation for disentangled graph representation learning.