Drift-Feature-Performance Decomposition in MI-EEG via Structured Geometric Modeling

Abstract

The reliability of Motor Imagery BCI is plagued by temporal non-stationarity: signal properties drift over time, causing decoding accuracy to decay. Existing solutions often treat this drift generically, failing to distinguish whether performance drops are driven by changes in sensorimotor activity itself or by distortions introduced during feature extraction.

This research introduces a framework to diagnostically decompose these drift pathways. Instead of proposing another black-box adaptation algorithm, we provide a structured method to isolate how non-stationarity propagates through specific elements of the BCI processing chain.

Methodological Framework

1. Geometric Modeling on the Manifold

We analyze the evolution of EEG covariance matrices on the Riemannian manifold of Symmetric Positive Definite (SPD) matrices. A unified preprocessing protocol based on trace normalization is imposed to project all data onto a common unit-trace manifold. This crucial step isolates geometric structural changes from simple magnitude fluctuations.

2. Two-Stage Drift Decomposition

We model drift propagation in two distinctive stages:

• Raw Drift ($X’$): Quantifies temporal variability in the raw sensor space, anchored to conditional Karcher means.
• Feature Drift ($M’$): We model the mapping from raw drift to feature space, identifying a “Compression Ratio”. The residual component, Residual Feature Drift ($M^\perp$), captures geometric distortions that are orthogonal to raw input changes—often the silent killer of BCI performance.

3. Algorithmic Interpretation (Grassmannian Geometry)

For spatial filtering methods like Common Spatial Patterns (CSP), we provide a theoretical interpretation of drift as a subspace misalignment. We quantify the divergence between fixed baseline filters and time-varying optimal filters using the projection metric on the Grassmann manifold, linking abstract geometric drift to concrete filter suboptimality.

Key Contribution: The Robustness Atlas

The framework culminates in the construction of a “Robustness Atlas”. This diagnostic map benchmarks BCI pipelines based on two coordinates:

1. Drift Compression: The pipeline’s ability to absorb raw sensor variability.
2. Sensitivity: The pipeline’s vulnerability to residual geometric distortions.

This Atlas provides actionable guidance: pipelines sensitive to raw drift motivate classifier retraining (Domain Adaptation), whereas those sensitive to residual distortion indicate a need to recalibrate the feature extractor.

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