# Learning to Model the Relationship Between Brain Structural and Functional Connectomes

arXiv: https://arxiv.org/abs/2112.09906 · HTML: https://mlsanity.com/paper/2112.09906/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 76 references that are in the map.
- First posted on arXiv 18 Dec 2021.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [Design Space for Graph Neural Networks](https://mlsanity.com/paper/2011.08843/) (2020)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [Discriminative Embeddings of Latent Variable Models for Structured Data](https://mlsanity.com/paper/1603.05629/) (2016)
- [Disease Prediction using Graph Convolutional Networks: Application to Autism Spectrum Disorder and Alzheimer's Disease](https://mlsanity.com/paper/1806.01738/) (2018)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Learning Dynamic Graph Representation of Brain Connectome with Spatio-Temporal Attention](https://mlsanity.com/paper/2105.13495/) (2021)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Spatio-Temporal Graph Convolution for Resting-State fMRI Analysis](https://mlsanity.com/paper/2003.10613/) (2020)
- [Graph Embedding on Biomedical Networks: Methods, Applications, and Evaluations](https://mlsanity.com/paper/1906.05017/) (2019)
- [Understanding Graph Isomorphism Network for rs-fMRI Functional Connectivity Analysis](https://mlsanity.com/paper/2001.03690/) (2020)

## Built on by (most cited first, 5 of 5)

- [SFC-GAN: A Generative Adversarial Network for Brain Functional and Structural Connectome Translation](https://mlsanity.com/paper/2501.07055/) (2025)
- [JGAT: a joint spatio-temporal graph attention model for brain decoding](https://mlsanity.com/paper/2306.05286/) (2023)
- [Cascaded two-stage feature clustering and selection via separability and consistency in fuzzy decision systems](https://mlsanity.com/paper/2407.15893/) (2024)
- [Graph Contrastive Learning for Connectome Classification](https://mlsanity.com/paper/2502.05109/) (2025)
- [Sex-based Network-Specific Differences in Connectomes: A Krakencoder-Based Analysis](https://mlsanity.com/paper/2606.16294/) (2026)

## Abstract (arXiv)

Recent advances in neuroimaging along with algorithmic innovations in statistical learning from network data offer a unique pathway to integrate brain structure and function, and thus facilitate revealing some of the brain's organizing principles at the system level. In this direction, we develop a supervised graph representation learning framework to model the relationship between brain structural connectivity (SC) and functional connectivity (FC) via a graph encoder-decoder system, where the SC is used as input to predict empirical FC. A trainable graph convolutional encoder captures direct and indirect interactions between brain regions-of-interest that mimic actual neural communications, as well as to integrate information from both the structural network topology and nodal (i.e., region-specific) attributes. The encoder learns node-level SC embeddings which are combined to generate (whole brain) graph-level representations for reconstructing empirical FC networks. The proposed end-to-end model utilizes a multi-objective loss function to jointly reconstruct FC networks and learn discriminative graph representations of the SC-to-FC mapping for downstream subject (i.e., graph-level) classification. Comprehensive experiments demonstrate that the learnt representations of said relationship capture valuable information from the intrinsic properties of the subject's brain networks and lead to improved accuracy in classifying a large population of heavy drinkers and non-drinkers from the Human Connectome Project. Our work offers new insights on the relationship between brain networks that support the promising prospect of using graph representation learning to discover more about human brain activity and function.