Subspace oddity - optimization on product of Stiefel manifolds for EEG data (2021)
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1 Abstract
Dimensionality reduction of high-dimensional electroencephalography (EEG) covariance matrices is crucial for effective utilization of Riemannian geometry in Brain-Computer Interfaces (BCI). In this paper, we propose a novel similarity-based classification method that relies on dimensionality reduction of EEG covariance matrices. Conventionally, the dimension of the original high-dimensional space is reduced by projecting into one low-dimensional space, and the similarity is learned only based on the single space. In contrast, our method, MUltiple SUbspace MDM Estimation (MUSUME), obtains multiple low-dimensional spaces that enhance class separability by solving the proposed optimization problem, then the similarity is learned in each low-dimensional space. This multiple projection approach encourages finding the space that is more useful for similarity learning. Experimental evaluation with high-dimensionality EEG datasets (128 channels) confirmed that MUSUME proved significant improvement for classification (p < 0.001) and also it showed the potential to beat the existing method relying on only one subspace representation.
2 NOTES
In this work the authors propose an improvement over another papers works. They take notice that in there is a proposal of a technique which can measure similarity between matrices, therefore, they can use another technique, which reduces the dimensionality of covariance matrices by projecting them into a low-dimensional subspace. However, the authors here go further, and instead propose using multiple low-dimensional subspaces, projecting the data into them and looking at each of them and seeing which provides the highest classification performance (similarity). This process of dimensionality reduction is done over an optimization procedure, solved using conjugate gradient and adaptive line search. Their result is better then simply using MDRM to classify covariance matrices for both testes datasets, with an average improvement of over 8% in MunichMI and 3% on HGD. I like their idea of using multiple subspaces and each one having a dimensionality reduction, seems like it could be better used, but not sure how yet.