Weakly supervised covariance matrices alignment through Stiefel matrices
  estimation for MEG applications
Antoine Collas Rémi Flamary Alexandre Gramfort
This paper introduces a novel domain adaptation technique for time series
data, called Mixing model Stiefel Adaptation (MSA), specifically addressing the
challenge of limited labeled signals in the target dataset. Leveraging a
domain-dependent mixing model and the optimal transport domain adaptation
assumption, we exploit abundant unlabeled data in the target domain to ensure
effective prediction by establishing pairwise correspondence with equivalent
signal variances between domains. Theoretical foundations are laid for
identifying crucial Stiefel matrices, essential for recovering underlying
signal variances from a Riemannian representation of observed signal
covariances. We propose an integrated cost function that simultaneously learns
these matrices, pairwise domain relationships, and a predictor, classifier, or
regressor, depending on the task. Applied to neuroscience problems, MSA
outperforms recent methods in brain-age regression with task variations using
magnetoencephalography (MEG) signals from the Cam-CAN dataset.