# Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networks

arXiv: https://arxiv.org/abs/1703.02161 · HTML: https://mlsanity.com/paper/1703.02161/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2017.

## Built on by (most cited first, 30 of 40)

- [Learning Dynamic Graph Representation of Brain Connectome with Spatio-Temporal Attention](https://mlsanity.com/paper/2105.13495/) (2021)
- [Graph-Based Deep Learning for Medical Diagnosis and Analysis: Past, Present and Future](https://mlsanity.com/paper/2105.13137/) (2021)
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- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [Online Graph Dictionary Learning](https://mlsanity.com/paper/2102.06555/) (2021)
- [Semi-relaxed Gromov-Wasserstein divergence with applications on graphs](https://mlsanity.com/paper/2110.02753/) (2021)
- [Brain Diffuser: An End-to-End Brain Image to Brain Network Pipeline](https://mlsanity.com/paper/2303.06410/) (2023)
- [Template based Graph Neural Network with Optimal Transport Distances](https://mlsanity.com/paper/2205.15733/) (2022)
- [Hypergraph-based Multi-View Action Recognition using Event Cameras](https://mlsanity.com/paper/2403.19316/) (2024)
- [Half-Hop: A graph upsampling approach for slowing down message passing](https://mlsanity.com/paper/2308.09198/) (2023)
- [Contrasformer: A Brain Network Contrastive Transformer for Neurodegenerative Condition Identification](https://mlsanity.com/paper/2409.10944/) (2024)
- [Learning Multi-Attention Context Graph for Group-Based Re-Identification](https://mlsanity.com/paper/2104.14236/) (2021)
- [Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More](https://mlsanity.com/paper/2107.06876/) (2021)
- [DecGAN: Decoupling Generative Adversarial Network detecting abnormal neural circuits for Alzheimer's disease](https://mlsanity.com/paper/2110.05712/) (2021)
- [Graph Classification via Reference Distribution Learning: Theory and Practice](https://mlsanity.com/paper/2408.11370/) (2024)
- [LEGO-Learn: Label-Efficient Graph Open-Set Learning](https://mlsanity.com/paper/2410.16386/) (2024)
- [A deep learning model for data-driven discovery of functional connectivity](https://mlsanity.com/paper/2112.04013/) (2021)
- [More Interpretable Graph Similarity Computation via Maximum Common Subgraph Inference](https://mlsanity.com/paper/2208.04580/) (2022)
- [BrainOOD: Out-of-distribution Generalizable Brain Network Analysis](https://mlsanity.com/paper/2502.01688/) (2025)
- [Multi-Atlas Brain Network Classification through Consistency Distillation and Complementary Information Fusion](https://mlsanity.com/paper/2410.08228/) (2024)
- [ClusterViG: Efficient Globally Aware Vision GNNs via Image Partitioning](https://mlsanity.com/paper/2501.10640/) (2025)
- [Contrastive Graph Pooling for Explainable Classification of Brain Networks](https://mlsanity.com/paper/2307.11133/) (2023)
- [Recovering Missing Node Features with Local Structure-based Embeddings](https://mlsanity.com/paper/2309.09068/) (2023)
- [Image complexity based fMRI-BOLD visual network categorization across visual datasets using topological descriptors and deep-hybrid learning](https://mlsanity.com/paper/2311.08417/) (2023)
- [Graph similarity learning for change-point detection in dynamic networks](https://mlsanity.com/paper/2203.15470/) (2022)
- [Benchmarking Graph Neural Networks for FMRI analysis](https://mlsanity.com/paper/2211.08927/) (2022)
- [Joint Self-Supervised and Supervised Contrastive Learning for Multimodal MRI Data: Towards Predicting Abnormal Neurodevelopment](https://mlsanity.com/paper/2312.15064/) (2023)
- [Deep Dynamic Effective Connectivity Estimation from Multivariate Time Series](https://mlsanity.com/paper/2202.02393/) (2022)
- [MHATC: Autism Spectrum Disorder identification utilizing multi-head attention encoder along with temporal consolidation modules](https://mlsanity.com/paper/2201.00404/) (2021)
- [ConnectomeDiffuser: Generative AI Enables Brain Network Construction from Diffusion Tensor Imaging](https://mlsanity.com/paper/2505.22683/) (2025)

## Abstract (arXiv)

Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance or similarity metric is, however, not trivial and can be highly dependent on the application at hand. In this work, we propose a novel metric learning method to evaluate distance between graphs that leverages the power of convolutional neural networks, while exploiting concepts from spectral graph theory to allow these operations on irregular graphs. We demonstrate the potential of our method in the field of connectomics, where neuronal pathways or functional connections between brain regions are commonly modelled as graphs. In this problem, the definition of an appropriate graph similarity function is critical to unveil patterns of disruptions associated with certain brain disorders. Experimental results on the ABIDE dataset show that our method can learn a graph similarity metric tailored for a clinical application, improving the performance of a simple k-nn classifier by 11.9% compared to a traditional distance metric.