Transferring Spatial Filters via Tangent Space Alignment in Motor Imagery BCIs

TL;DR

This work tackles subject transfer in motor imagery BCIs by uniting Riemannian geometry with CSP. Covariance matrices are aligned in a tangent space via Log/Exp maps around Riemannian means, enabling a CSP-based filter to be learned on aligned data and transferred to the target subject. Three multi-subject transfer schemes (RTCSP-SSF, RTCSP-Combine, RTCSP-Ensemble) demonstrate that tangent-space alignment can improve generalization, especially when target data are scarce, and can outperform standard CSP and some prior domain-adaptation methods. The approach offers practical benefits for rapid calibration in data-limited settings, with future avenues including contrastive learning on SPD manifolds and geometry-aware neural architectures to further leverage covariance representations.

Abstract

We propose a method to improve subject transfer in motor imagery BCIs by aligning covariance matrices on a Riemannian manifold, followed by computing a new common spatial patterns (CSP) based spatial filter. We explore various ways to integrate information from multiple subjects and show improved performance compared to standard CSP. Across three datasets, our method shows marginal improvements over standard CSP; however, when training data are limited, the improvements become more significant.

Figures (5)

• Figure 1: A comparison of features resulting from standard CSP with RTCSP-SSF and RTCSP-Combine. The spatial filter in each plot was obtained with training data and the same filter was used on both train and test data to obtain the resulting features. The ellipses represent the contours of the bi-variate normal distribution of features associated with each class of motor imagery at one standard deviation per axis. Ellipses associated with training data are solid colors, while ellipses associated with test data are the same color, but darker and with dashed lines. Decision boundaries for both the training and test data are shown. Test labels were only accessed for the purposes of this figure.
• Figure 2: Spatial patterns for standard CSP and RTCSP-SSF, showing how presumed neural sources project onto the scalp at each electrode. Polarity reflects the relative contribution of each source to the measured signals in sensor space. Generalized eigenvalues from the CSP problem were ordered from highest to lowest, and we plot one spatial filter associated with the three largest eigenvalues, and one filter from the three smallest.
• Figure 3: Performance of our methods when different amounts of training data are available for the target subject. Our methods generalize to unseen data in low training data regimes more effectively than standard CSP.
• Figure 4: The ratio of maximum to minimum projected variances on datasets three and BCIC-III 4a, averaged over trials and subjects. This quantity reflects a spatial filter's ability to generalize and create discriminative features on unseen data, enabling more accurate classification. Standard CSP requires a larger amount of training data to generalize effectively, whereas RTCSP-SSF achieves similar performance with substantially less data. Error bars represent the standard error across 50 runs. Refer to Fig. 5 for the distribution corresponding to the left-most bars (20% of training data used).
• Figure 5: Example of 50 runs of the described experiment when 20% of target training data is used. These distributions correspond with the left most bars on figure 4.