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arXiv · 2504.18882

SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges

Ce Ju·Reinmar Kobler·Antoine Collas·Motoaki Kawanabe·Cuntai Guan·Bertrand Thirion
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Abstract

Neuroimaging provides essential tools for characterizing brain activity, structure, and connectivity through modalities that capture complementary aspects of brain organization. Across these diverse modalities, a unifying perspective arises when measurements are modeled as symmetric positive-definite (SPD)-valued representations through appropriate estimation or regularization procedures. Endowed with Riemannian geometry, the SPD manifold provides a non-Euclidean framework for principled statistical inference and machine learning on these representations. This review organizes these analytical and learning approaches within a framework for SPD matrix learning that connects classical geometric statistics with modern machine learning across neuroimaging and neurophysiological applications. We systematically survey the progression from modality-specific representations to geometric shallow and deep learning paradigms, highlighting how SPD matrix learning preserves underlying structural constraints while extending to modern AI applications in neuroimaging and brain-computer interfaces.

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Ce Ju, Reinmar Kobler, Antoine Collas, Motoaki Kawanabe, Cuntai Guan, Bertrand Thirion. 2026-08-21. SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges. https://doi.org/10.1109/tpami.2026.3726269

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