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

[Submitted on 26 Apr 2025 (v1), last revised 21 Aug 2026 (this version, v3)]

View PDF HTML (experimental)

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.

Submission history

From: Ce Ju [view email]
[v1] Sat, 26 Apr 2025 10:05:04 UTC (1,409 KB)
[v2] Wed, 7 Jan 2026 00:00:11 UTC (1,675 KB)
[v3] Fri, 21 Aug 2026 12:22:12 UTC (2,032 KB)