# Aligning individual brains with Fused Unbalanced Gromov-Wasserstein

arXiv: https://arxiv.org/abs/2206.09398 · HTML: https://mlsanity.com/paper/2206.09398/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 53 references that are in the map.
- First posted on arXiv 19 Jun 2022.

## Builds on (most cited first, 8 of 8)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Machine Learning for Neuroimaging with Scikit-Learn](https://mlsanity.com/paper/1412.3919/) (2014)
- [The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation](https://mlsanity.com/paper/2009.04266/) (2020)
- [Unbalanced Optimal Transport through Non-negative Penalized Linear Regression](https://mlsanity.com/paper/2106.04145/) (2021)
- [Fast Optimal Transport Averaging of Neuroimaging Data](https://mlsanity.com/paper/1503.08596/) (2015)
- [Modeling Shared Responses in Neuroimaging Studies through MultiView ICA](https://mlsanity.com/paper/2006.06635/) (2020)

## Built on by (most cited first, 23 of 23)

- [MindEye2: Shared-Subject Models Enable fMRI-To-Image With 1 Hour of Data](https://mlsanity.com/paper/2403.11207/) (2024)
- [Temporally Consistent Unbalanced Optimal Transport for Unsupervised Action Segmentation](https://mlsanity.com/paper/2404.01518/) (2024)
- [GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics](https://mlsanity.com/paper/2310.09254/) (2023)
- [Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein](https://mlsanity.com/paper/2402.02239/) (2024)
- [Joint Self-Supervised Video Alignment and Action Segmentation](https://mlsanity.com/paper/2503.16832/) (2025)
- [Unbalanced Low-rank Optimal Transport Solvers](https://mlsanity.com/paper/2305.19727/) (2023)
- [Any2Graph: Deep End-To-End Supervised Graph Prediction With An Optimal Transport Loss](https://mlsanity.com/paper/2402.12269/) (2024)
- [BRACTIVE: A Brain Activation Approach to Human Visual Brain Learning](https://mlsanity.com/paper/2405.18808/) (2024)
- [SUGAR: Spherical Ultrafast Graph Attention Framework for Cortical Surface Registration](https://mlsanity.com/paper/2307.00511/) (2023)
- [Brainformer: Mimic Human Visual Brain Functions to Machine Vision Models via fMRI](https://mlsanity.com/paper/2312.00236/) (2023)
- [Across-subject ensemble-learning alleviates the need for large samples for fMRI decoding](https://mlsanity.com/paper/2407.12056/) (2024)
- [Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphs](https://mlsanity.com/paper/2506.12025/) (2025)
- [Efficient Multi Subject Visual Reconstruction from fMRI Using Aligned Representations](https://mlsanity.com/paper/2505.01670/) (2025)
- [Biomechanical-phase based Temporal Segmentation in Sports Videos: a Demonstration on Javelin-Throw](https://mlsanity.com/paper/2509.24606/) (2025)
- [Neural Correlates of Language Models Are Specific to Human Language](https://mlsanity.com/paper/2510.03156/) (2025)
- [Unsupervised Multimodal Surface Registration with Geometric Deep Learning](https://mlsanity.com/paper/2311.13022/) (2023)
- [Optimizing fMRI Data Acquisition for Decoding Natural Speech with Limited Participants](https://mlsanity.com/paper/2505.21304/) (2025)
- [Helping CLIP See Both the Forest and the Trees: A Decomposition and Description Approach](https://mlsanity.com/paper/2507.03458/) (2025)
- [Learning local and global prototypes with optimal transport for unsupervised anomaly detection and localization](https://mlsanity.com/paper/2508.12927/) (2025)
- [Structured Matching via Cost-Regularized Unbalanced Optimal Transport](https://mlsanity.com/paper/2511.19075/) (2025)
- [Gromov Wasserstein Optimal Transport for Semantic Correspondences](https://mlsanity.com/paper/2602.03105/) (2026)
- [Learning fMRI activations dictionaries across individual geometries via optimal transport](https://mlsanity.com/paper/2605.20883/) (2026)
- [Fast Whole-Brain, Geometry-Aware Functional Alignment for Cross-Subject Decoding](https://mlsanity.com/paper/2607.10931/) (2026)

## Abstract (arXiv)

Individual brains vary in both anatomy and functional organization, even within a given species. Inter-individual variability is a major impediment when trying to draw generalizable conclusions from neuroimaging data collected on groups of subjects. Current co-registration procedures rely on limited data, and thus lead to very coarse inter-subject alignments. In this work, we present a novel method for inter-subject alignment based on Optimal Transport, denoted as Fused Unbalanced Gromov Wasserstein (FUGW). The method aligns cortical surfaces based on the similarity of their functional signatures in response to a variety of stimulation settings, while penalizing large deformations of individual topographic organization. We demonstrate that FUGW is well-suited for whole-brain landmark-free alignment. The unbalanced feature allows to deal with the fact that functional areas vary in size across subjects. Our results show that FUGW alignment significantly increases between-subject correlation of activity for independent functional data, and leads to more precise mapping at the group level.