@mellotPhysicsinformedUnsupervisedRiemannian2024

Physics-informed and Unsupervised Riemannian Domain Adaptation for Machine Learning on Heterogeneous EEG Datasets (2024)

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1 Abstract

Combining electroencephalogram (EEG) datasets for supervised machine learning (ML) is challenging due to session, subject, and device variability. ML algorithms typically require identical features at train and test time, complicating analysis due to varying sensor numbers and positions across datasets. Simple channel selection discards valuable data, leading to poorer performance, especially with datasets sharing few channels. To address this, we propose an unsupervised approach leveraging EEG signal physics. We map EEG channels to fixed positions using field interpolation, facilitating source-free domain adaptation. Leveraging Riemannian geometry classification pipelines and transfer learning steps, our method demonstrates robust performance in brain-computer interface (BCI) tasks and potential biomarker applications. Comparative analysis against a statistical-based approach known as Dimensionality Transcending, a signal-based imputation called ComImp, source-dependent methods, as well as common channel selection and spherical spline interpolation, was conducted with leave-one-dataset-out validation on six public BCI datasets for a right-hand/left-hand classification task. Numerical experiments show that in the presence of few shared channels in train and test, the field interpolation consistently outperforms other methods, demonstrating enhanced classification performance across all datasets. When more channels are shared, field interpolation was found to be competitive with other methods and faster to compute than source-dependent methods.

2 NOTES

In this paper the authors propose a method to perform cross-dataset classification even for datasets where the number of channels are different. Their idea is similar to Dimensionality Transcending, that is, to construct a covariance matrix that has size equal to the largest number of electrodes of one of the datasets. However, in here the idea is based on interpolation, but rather than a simple one, they rely on those that are physics-informed and can that advantage of the position of the electrodes. To do it they first set a pre-determined position for the electrodes. Then they apply two techniques separately (and compare them): Spherical Spline Interpolation (SSI) and Field Interpolation (FI). The first one, SSI, comes from a paper from 1989, which projects the electrodes initial and desired final positions onto a linear sphere, then the linear mapping matrix ($\hat{\mathbf{X}}=\mathbf{AX}$) is used to interpolate the signal at the desired position based on the existing signal. The second, FI, is based on Maxwell’s equations, seems to be more complex and has no further explanation on the paper other than saying it generates electric potential estimates by mapping the data to brain space using a Tikhonov regularization (referred to as Minimum Norm Estimate - MNE).

Quotes:

Interpolation

Interpolation involves constructing a linear operator $\mathbf{A}\in {\mathbb{R}}^{P\times P_j}$ that maps the $P_j$ existing EEG channels to the $P$ positions of a fixed template:
$\hat{\mathbf{X}}=\mathbf{AX},$
where $\mathbf{X}\in {\mathbb{R}}^{P_j\times T}$ are the recorded EEG signals and $\hat{\mathbf{X}}\in {\mathbb{R}}^{P\times T}$ are the reconstructed signals.