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SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG

Shanglin Li, Motoaki Kawanabe, Reinmar J. Kobler

TL;DR

The paper addresses EEG generalization under non-stationarity by formulating SFUDA with label shifts and proposing SPDIM, a geometry-aware, parameter-efficient approach operating on the SPD manifold. It shows that traditional Fréchet-mean alignment (RCT+TSM) can compensate conditional shifts but worsen under label shifts, and introduces a domain-specific SPD bias learned via Information Maximization to counter over-corrections. The method combines Tangent Space Mapping, SPD batch norm, and a manifold-constrained bias to achieve robust cross-domain adaptation, validated on simulated data and public EEG motor imagery and sleep staging datasets. The results indicate SPDIM often achieves top performance in cross-session and cross-subject transfers, offering a practical pathway for label-shift-aware SFUDA in EEG neurotechnology."

Abstract

The non-stationary nature of electroencephalography (EEG) introduces distribution shifts across domains (e.g., days and subjects), posing a significant challenge to EEG-based neurotechnology generalization. Without labeled calibration data for target domains, the problem is a source-free unsupervised domain adaptation (SFUDA) problem. For scenarios with constant label distribution, Riemannian geometry-aware statistical alignment frameworks on the symmetric positive definite (SPD) manifold are considered state-of-the-art. However, many practical scenarios, including EEG-based sleep staging, exhibit label shifts. Here, we propose a geometric deep learning framework for SFUDA problems under specific distribution shifts, including label shifts. We introduce a novel, realistic generative model and show that prior Riemannian statistical alignment methods on the SPD manifold can compensate for specific marginal and conditional distribution shifts but hurt generalization under label shifts. As a remedy, we propose a parameter-efficient manifold optimization strategy termed SPDIM. SPDIM uses the information maximization principle to learn a single SPD-manifold-constrained parameter per target domain. In simulations, we demonstrate that SPDIM can compensate for the shifts under our generative model. Moreover, using public EEG-based brain-computer interface and sleep staging datasets, we show that SPDIM outperforms prior approaches.

SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG

TL;DR

The paper addresses EEG generalization under non-stationarity by formulating SFUDA with label shifts and proposing SPDIM, a geometry-aware, parameter-efficient approach operating on the SPD manifold. It shows that traditional Fréchet-mean alignment (RCT+TSM) can compensate conditional shifts but worsen under label shifts, and introduces a domain-specific SPD bias learned via Information Maximization to counter over-corrections. The method combines Tangent Space Mapping, SPD batch norm, and a manifold-constrained bias to achieve robust cross-domain adaptation, validated on simulated data and public EEG motor imagery and sleep staging datasets. The results indicate SPDIM often achieves top performance in cross-session and cross-subject transfers, offering a practical pathway for label-shift-aware SFUDA in EEG neurotechnology."

Abstract

The non-stationary nature of electroencephalography (EEG) introduces distribution shifts across domains (e.g., days and subjects), posing a significant challenge to EEG-based neurotechnology generalization. Without labeled calibration data for target domains, the problem is a source-free unsupervised domain adaptation (SFUDA) problem. For scenarios with constant label distribution, Riemannian geometry-aware statistical alignment frameworks on the symmetric positive definite (SPD) manifold are considered state-of-the-art. However, many practical scenarios, including EEG-based sleep staging, exhibit label shifts. Here, we propose a geometric deep learning framework for SFUDA problems under specific distribution shifts, including label shifts. We introduce a novel, realistic generative model and show that prior Riemannian statistical alignment methods on the SPD manifold can compensate for specific marginal and conditional distribution shifts but hurt generalization under label shifts. As a remedy, we propose a parameter-efficient manifold optimization strategy termed SPDIM. SPDIM uses the information maximization principle to learn a single SPD-manifold-constrained parameter per target domain. In simulations, we demonstrate that SPDIM can compensate for the shifts under our generative model. Moreover, using public EEG-based brain-computer interface and sleep staging datasets, we show that SPDIM outperforms prior approaches.

Paper Structure

This paper contains 30 sections, 2 theorems, 28 equations, 7 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. SFUDA Scenario
  4. Riemannian Geometry on $\mathcal{S}^{+}_{D}$
  5. Methods
  6. Generative Model
  7. Decoding Framework
  8. Tangent space mapping (TSM) to recover $\log(E_i)$
  9. RCT+TSM compensates marginal and conditional shifts
  10. Alignment under label shifts
  11. Latent alignment with domain-specific SPD batch norm.
  12. SPD Manifold Information Maximization
  13. Experiments
  14. Simulations
  15. EEG Motor Imagery Data
  16. ...and 15 more sections

Key Result

Proposition 1

Given the specified generative model and a set of examples $\mathcal{E}_j = \{ (E_i, y_i, j) | E_i \in \mathcal{S}_P^+, y_i \in \mathcal{Y} \}_{i \leq M_j}$ of domain $j \in \mathcal{J}$, we have that the Fréchet mean of $\mathcal{E}_j$, defined in (eq_FM), converges to the identity matrix $I_P$ wit

Figures (7)

  • Figure 1: Framework Overview. a, EEG data $\mathrm{x}$ is generated by mixing source signals $\mathrm{z}$ with unknown, linear forward models $A_{\mathrm{j}}$. A submanifold $\mathcal{S}_D^+$ of the sources' covariance matrices $\mathrm{E} \in \mathcal{S}_P^+$ encodes information about the label $y$. Domain-specific label priors $\pi_j$ and forward models $A_j$ introduce label and conditional distribution shifts, respectively. b, Multi-source domain training, utilizes balanced batch sampling and the end-to-end latent alignment framework proposed in kobler2022spd. c, Proposed SPDIM framework. After latent alignment of marginal distributions (step 1), SPDIM uses the information maximization (IM) loss to fit a bias parameter $\Phi_j \in \mathcal{S}_D^+$ (step 2), and thereby counteract over-corrections in step 1 that are driven by label shifts.
  • Figure 2: Simulation results. Balanced accuracy scores (higher is better) across target domain label ratios (i.e., majority to minority label ratio) on the x-axis and class separability $p(s|y)$ across panels. Source domain labels were balanced.
  • Figure 3: Motor-imagery results (0.2 label ratio). Average of test-set scores (balanced accuracy; higher is better; error bars indicate 95% confidence interval) relative to TSMNet+SPDSBN kobler2022spd w/o label shifts. For extended results per dataset, see Tables \ref{['tab_results_mi_ex_imbalanced']} and \ref{['tab_results_mi_ex_balanced']}.
  • Figure A1: Performance over the number of source domains. Same parameters as in Figure \ref{['fig_res_sim']} (panel 3) but for a different number of source domains $|\mathcal{J}_s| \in \lbrace 1, 3, 5, 7\rbrace$.
  • Figure A2: Performance over the number of samples per domain $M_j$. Same as Figure \ref{['fig_res_sim']} (panel 3) but for a different number of samples per domains $M_j \in \lbrace 100, 200, 400, 800\rbrace$.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Remark 1
  • Proposition 2
  • Remark 2