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

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.

18 pages, 2 figures, 2 tables; This work was accepted for publication in IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) in 2026. Copyright may be transferred without notice, after which this version may no longer be accessible