SPD Learning for Covariance-Based Neuroimaging Analysis: Perspectives, Methods, and Challenges

• URL: http://arxiv.org/abs/2504.18882v1
• Date: Sat, 26 Apr 2025 10:05:04 GMT
• Title: SPD Learning for Covariance-Based Neuroimaging Analysis: Perspectives, Methods, and Challenges
• Authors: Ce Ju, Reinmar J. Kobler, Antoine Collas, Motoaki Kawanabe, Cuntai Guan, Bertrand Thirion,
• Abstract summary: Neuroimaging provides a critical framework for characterizing brain activity by quantifying connectivity patterns and functional architecture across modalities.<n>Modern machine learning has significantly advanced our understanding of neural processing mechanisms through these datasets.<n>This review focuses on machine learning approaches for covariance-based neuroimaging data, where often symmetric positive definite (SPD) matrices under full-rank conditions encode inter-channel relationships.
• Score: 41.955864444491965
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neuroimaging provides a critical framework for characterizing brain activity by quantifying connectivity patterns and functional architecture across modalities. While modern machine learning has significantly advanced our understanding of neural processing mechanisms through these datasets, decoding task-specific signatures must contend with inherent neuroimaging constraints, for example, low signal-to-noise ratios in raw electrophysiological recordings, cross-session non-stationarity, and limited sample sizes. This review focuses on machine learning approaches for covariance-based neuroimaging data, where often symmetric positive definite (SPD) matrices under full-rank conditions encode inter-channel relationships. By equipping the space of SPD matrices with Riemannian metrics (e.g., affine-invariant or log-Euclidean), their space forms a Riemannian manifold enabling geometric analysis. We unify methodologies operating on this manifold under the SPD learning framework, which systematically leverages the SPD manifold's geometry to process covariance features, thereby advancing brain imaging analytics.

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