Geometry-Aware Deep Congruence Networks for Manifold Learning in Cross-Subject Motor Imagery

TL;DR

This paper introduces geometry-aware deep congruence networks that improve cross-subject motor imagery decoding in EEG-based brain-computer interfaces by addressing variability issues with novel congruence transforms and models.

Contribution

It proposes three new geometry-aware models for manifold learning that effectively mitigate inter-subject variability in EEG motor imagery decoding.

Findings

Improved cross-subject accuracy by 2-3% on benchmarks.

Effective as both pre-alignment modules and end-to-end systems.

Addresses dispersion scaling and orientation alignment issues.

Abstract

Cross-subject motor-imagery decoding remains a major challenge in EEG-based brain-computer interfaces. To mitigate strong inter-subject variability, recent work has emphasized manifold-based approaches operating on covariance representations. Yet dispersion scaling and orientation alignment remain largely unaddressed in existing methods. In this paper, we address both issues through congruence transforms and introduce three complementary geometry-aware models: (i) Discriminative Congruence Transform (DCT), (ii) Deep Linear DCT (DLDCT), and (iii) Deep DCT-UNet (DDCT-UNet). These models are evaluated both as pre-alignment modules for downstream classifiers and as end-to-end discriminative systems trained via cross-entropy backpropagation with a custom logistic-regression head. Across challenging motor-imagery benchmarks, the proposed framework improves transductive cross-subject accuracy by 2-3%, demonstrating the value of geometry-aware congruence learning.