# Deep Graph Normalizer: A Geometric Deep Learning Approach for Estimating Connectional Brain Templates

arXiv: https://arxiv.org/abs/2012.14131 · HTML: https://mlsanity.com/paper/2012.14131/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2020.

## Built on by (most cited first, 16 of 16)

- [Graph Neural Networks in Network Neuroscience](https://mlsanity.com/paper/2106.03535/) (2021)
- [Federated Graph Machine Learning: A Survey of Concepts, Techniques, and Applications](https://mlsanity.com/paper/2207.11812/) (2022)
- [MGN-Net: a multi-view graph normalizer for integrating heterogeneous biological network populations](https://mlsanity.com/paper/2104.03895/) (2021)
- [Brain Multigraph Prediction using Topology-Aware Adversarial Graph Neural Network](https://mlsanity.com/paper/2105.02565/) (2021)
- [Recurrent Brain Graph Mapper for Predicting Time-Dependent Brain Graph Evaluation Trajectory](https://mlsanity.com/paper/2110.11237/) (2021)
- [Graph-in-Graph (GiG): Learning interpretable latent graphs in non-Euclidean domain for biological and healthcare applications](https://mlsanity.com/paper/2204.00323/) (2022)
- [Comparative Survey of Multigraph Integration Methods for Holistic Brain Connectivity Mapping](https://mlsanity.com/paper/2204.05110/) (2022)
- [Recurrent Multigraph Integrator Network for Predicting the Evolution of Population-Driven Brain Connectivity Templates](https://mlsanity.com/paper/2110.03453/) (2021)
- [One Representative-Shot Learning Using a Population-Driven Template with Application to Brain Connectivity Classification and Evolution Prediction](https://mlsanity.com/paper/2110.11238/) (2021)
- [Deep Cross-Modality and Resolution Graph Integration for Universal Brain Connectivity Mapping and Augmentation](https://mlsanity.com/paper/2209.13529/) (2022)
- [Predicting Brain Multigraph Population From a Single Graph Template for Boosting One-Shot Classification](https://mlsanity.com/paper/2209.06005/) (2022)
- [Population Template-Based Brain Graph Augmentation for Improving One-Shot Learning Classification](https://mlsanity.com/paper/2212.07790/) (2022)
- [Multi-Sensory Cognitive Computing for Learning Population-level Brain Connectivity](https://mlsanity.com/paper/2508.11436/) (2025)
- [CogGNN: Cognitive Graph Neural Networks in Generative Connectomics](https://mlsanity.com/paper/2509.10864/) (2025)
- [Metadata-Driven Federated Learning of Connectional Brain Templates in Non-IID Multi-Domain Scenarios](https://mlsanity.com/paper/2403.09139/) (2024)
- [Graph Residual Noise Learner Network for Brain Connectivity Graph Prediction](https://mlsanity.com/paper/2410.00082/) (2024)

## Abstract (arXiv)

A connectional brain template (CBT) is a normalized graph-based representation of a population of brain networks also regarded as an average connectome. CBTs are powerful tools for creating representative maps of brain connectivity in typical and atypical populations. Particularly, estimating a well-centered and representative CBT for populations of multi-view brain networks (MVBN) is more challenging since these networks sit on complex manifolds and there is no easy way to fuse different heterogeneous network views. This problem remains unexplored with the exception of a few recent works rooted in the assumption that the relationship between connectomes are mostly linear. However, such an assumption fails to capture complex patterns and non-linear variation across individuals. Besides, existing methods are simply composed of sequential MVBN processing blocks without any feedback mechanism, leading to error accumulation. To address these issues, we propose Deep Graph Normalizer (DGN), the first geometric deep learning (GDL) architecture for normalizing a population of MVBNs by integrating them into a single connectional brain template. Our end-to-end DGN learns how to fuse multi-view brain networks while capturing non-linear patterns across subjects and preserving brain graph topological properties by capitalizing on graph convolutional neural networks. We also introduce a randomized weighted loss function which also acts as a regularizer to minimize the distance between the population of MVBNs and the estimated CBT, thereby enforcing its centeredness. We demonstrate that DGN significantly outperforms existing state-of-the-art methods on estimating CBTs on both small-scale and large-scale connectomic datasets in terms of both representativeness and discriminability (i.e., identifying distinctive connectivities fingerprinting each brain network population).