SPD Learning for Covariance-Based Neuroimaging Analysis: Perspectives, Methods, and Challenges
It addresses challenges in neuroimaging analysis, such as low signal-to-noise ratios and limited sample sizes, for researchers in brain imaging and machine learning, but is incremental as it reviews existing methods.
This review tackles the problem of analyzing covariance-based neuroimaging data, which involves SPD matrices, by unifying machine learning methods that use Riemannian geometry to process these features, thereby advancing brain imaging analytics.
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.