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

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13939)


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 Fréchet 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.


  • Functional Connectomics
  • SPD Manifolds
  • Fréchet Mean Estimation
  • Geometry-Aware Neural Networks

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This work is supported by the National Science Foundation CAREER award 1845430 (PI Venkataraman), the National Institute of Health R01HD108790 (PI Venkataraman) and R01EB029977 (PI Caffo).

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Correspondence to Niharika S. D’Souza .

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D’Souza, N.S., Venkataraman, A. (2023). mSPD-NN: A Geometrically Aware Neural Framework for Biomarker Discovery from Functional Connectomics Manifolds. In: Frangi, A., de Bruijne, M., Wassermann, D., Navab, N. (eds) Information Processing in Medical Imaging. IPMI 2023. Lecture Notes in Computer Science, vol 13939. Springer, Cham.

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