# Recurrent Multigraph Integrator Network for Predicting the Evolution of Population-Driven Brain Connectivity Templates

arXiv: https://arxiv.org/abs/2110.03453 · HTML: https://mlsanity.com/paper/2110.03453/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 6 Oct 2021.

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

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Graph Neural Networks in Network Neuroscience](https://mlsanity.com/paper/2106.03535/) (2021)
- [Deep Graph Normalizer: A Geometric Deep Learning Approach for Estimating Connectional Brain Templates](https://mlsanity.com/paper/2012.14131/) (2020)
- [Brain network similarity:Methods and applications](https://mlsanity.com/paper/1908.10592/) (2019)
- [Supervised Multi-topology Network Cross-diffusion for Population-driven Brain Network Atlas Estimation](https://mlsanity.com/paper/2009.11054/) (2020)

## Built on by (most cited first, 3 of 3)

- [Comparative Survey of Multigraph Integration Methods for Holistic Brain Connectivity Mapping](https://mlsanity.com/paper/2204.05110/) (2022)
- [Interpretable Spatio-Temporal Embedding for Brain Structural-Effective Network with Ordinary Differential Equation](https://mlsanity.com/paper/2405.13190/) (2024)
- [Population Template-Based Brain Graph Augmentation for Improving One-Shot Learning Classification](https://mlsanity.com/paper/2212.07790/) (2022)

## Abstract (arXiv)

Learning how to estimate a connectional brain template(CBT) from a population of brain multigraphs, where each graph (e.g., functional) quantifies a particular relationship between pairs of brain regions of interest (ROIs), allows to pin down the unique connectivity patterns shared across individuals. Specifically, a CBT is viewed as an integral representation of a set of highly heterogeneous graphs and ideally meeting the centeredness (i.e., minimum distance to all graphs in the population) and discriminativeness (i.e., distinguishes the healthy from the disordered population) criteria. So far, existing works have been limited to only integrating and fusing a population of brain multigraphs acquired at a single timepoint. In this paper, we unprecedentedly tackle the question: Given a baseline multigraph population, can we learn how to integrate and forecast its CBT representations at follow-up timepoints? Addressing such question is of paramount in predicting common alternations across healthy and disordered populations. To fill this gap, we propose Recurrent Multigraph Integrator Network (ReMI-Net), the first graph recurrent neural network which infers the baseline CBT of an input population t1 and predicts its longitudinal evolution over time (ti > t1). Our ReMI-Net is composed of recurrent neural blocks with graph convolutional layers using a cross-node message passing to first learn hidden-states embeddings of each CBT node (i.e., brain region of interest) and then predict its evolution at the consecutive timepoint. Moreover, we design a novel time-dependent loss to regularize the CBT evolution trajectory over time and further introduce a cyclic recursion and learnable normalization layer to generate well-centered CBTs from time-dependent hidden-state embeddings. Finally, we derive the CBT adjacency matrix from the learned hidden state graph representation.