# mSPD-NN: A Geometrically Aware Neural Framework for Biomarker Discovery from Functional Connectomics Manifolds

arXiv: https://arxiv.org/abs/2303.14986 · HTML: https://mlsanity.com/paper/2303.14986/

## Key facts

- Cited by 1 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 27 Mar 2023.

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

- [Graph Neural Networks in Network Neuroscience](https://mlsanity.com/paper/2106.03535/) (2021)
- [A neural network based on SPD manifold learning for skeleton-based hand gesture recognition](https://mlsanity.com/paper/1904.12970/) (2019)
- [Machine learning in resting-state fMRI analysis](https://mlsanity.com/paper/1812.11477/) (2018)
- [A Matrix Autoencoder Framework to Align the Functional and Structural Connectivity Manifolds as Guided by Behavioral Phenotypes](https://mlsanity.com/paper/2105.14409/) (2021)
- [A Joint Network Optimization Framework to Predict Clinical Severity from Resting State Functional MRI Data](https://mlsanity.com/paper/2009.03238/) (2020)
- [A Multi-Task Deep Learning Framework to Localize the Eloquent Cortex in Brain Tumor Patients Using Dynamic Functional Connectivity](https://mlsanity.com/paper/2011.08813/) (2020)
- [Integrating Neural Networks and Dictionary Learning for Multidimensional Clinical Characterizations from Functional Connectomics Data](https://mlsanity.com/paper/2007.01930/) (2020)
- [A Majorization-Minimization Algorithm for Computing the Karcher Mean of Positive Definite Matrices](https://mlsanity.com/paper/1312.4654/) (2013)
- [Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices](https://mlsanity.com/paper/1505.07343/) (2015)

## Built on by (most cited first, 1 of 1)

- [Geo-UNet: A Geometrically Constrained Neural Framework for Clinical-Grade Lumen Segmentation in Intravascular Ultrasound](https://mlsanity.com/paper/2408.04826/) (2024)

## Abstract (arXiv)

Connectomics has emerged as a powerful tool in neuroimaging and has spurred recent advancements in statistical and machine learning methods for connectivity data. Despite connectomes inhabiting a matrix manifold, most analytical frameworks ignore the underlying data geometry. This is largely because simple operations, such as mean estimation, do not have easily computable closed-form solutions. We propose a geometrically aware neural framework for connectomes, i.e., the mSPD-NN, designed to estimate the geodesic mean of a collections of symmetric positive definite (SPD) matrices. The mSPD-NN is comprised of bilinear fully connected layers with tied weights and utilizes a novel loss function to optimize the matrix-normal equation arising from Fr'echet mean estimation. Via experiments on synthetic data, we demonstrate the efficacy of our mSPD-NN against common alternatives for SPD mean estimation, providing competitive performance in terms of scalability and robustness to noise. We illustrate the real-world flexibility of the mSPD-NN in multiple experiments on rs-fMRI data and demonstrate that it uncovers stable biomarkers associated with subtle network differences among patients with ADHD-ASD comorbidities and healthy controls.