LGC-RCT — Local Geometric Consistency + Riemannian Centering Transformation

Unsupervised transductive cross-subject EEG transfer learning for passive Brain-Computer Interfaces.

Licona Muñoz, R., Guetschel, P., Bruin, J., Yilmaz, E. & Brouwer, A.-M. — "Local Geometric Consistency for Cross-Subject EEG Transfer Learning" NAT 2026, Berlin. (citation forthcoming)

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What is LGC-RCT?

LGC-RCT is an unsupervised transductive method for cross-subject EEG transfer learning designed for passive BCI applications. It combines two components:

• RCT (Riemannian Centering Transformation) [1]: a transfer learning method that re-centers covariance representations across domains to the identity matrix. Domains are treated as independent prior to the re-centering and classification phases.

• LGC (Local Geometric Consistency) (proposed): a local-geometry phase applied prior to RCT. For each covariance matrix, a neighborhood including its immediate temporal neighbors on both sides is defined. A local Riemannian mean is computed over this neighborhood, and the matrix is replaced by this local estimate. The parameter K controls the degree of local geometric consistency enforced between neighboring window-level covariance matrices.

In this work, we investigate whether enforcing local geometric consistency among neighboring covariance matrices prior to RCT improves cross-subject workload classification.

Pipeline

Notation — used consistently throughout the diagram:

• S : number of subjects (domains)
• C : number of EEG channels
• T : number of time samples per window
• N : total number of windows across all subjects (N = S × trials × windows_per_trial)
• [f_lo, f_hi] : frequency band (Hz) — dataset-specific (e.g. 8–12 Hz, 15–36 Hz)

 Continuous EEG — S subjects · C channels · [f_lo, f_hi] Hz band
        │  shape per subject: (C, T_total)
        ▼
 ┌─────────────────────────────────────────────────────────────┐
 │  Band-pass filter  [f_lo, f_hi] Hz (Butterworth order 4)   │
 │  + Sliding windows (4 s · 50% overlap · 128 Hz)             │
 └─────────────────────────────────────────────────────────────┘
        │  (N, C, T)   — N windows across all subjects
        ▼
 ┌─────────────────────────────────────────────────────────────┐
 │  Covariance matrix estimation                               │
 │  Ledoit-Wolf · pyriemann Covariances('lwf')                 │
 └─────────────────────────────────────────────────────────────┘
        │  (N, C, C)   — N symmetric positive-definite matrices
        ▼
 ╔═════════════════════════════════════════════════════════════╗
 ║  LGC — Local Geometric Consistency          [proposed]      ║
 ║  Replaces each C_i with the Riemannian mean of its          ║
 ║  K nearest temporal neighbors within the same class segment ║
 ╚═════════════════════════════════════════════════════════════╝
        │  (N, C, C)   — LGC-processed SPD matrices
        ▼
 ┌─────────────────────────────────────────────────────────────┐
 │  RCT — Riemannian Centering Transformation                  │
 │  Re-centers each domain to the identity matrix              │
 └─────────────────────────────────────────────────────────────┘
        │  (N, C, C)   — domain-aligned SPD matrices
        ▼
 ┌─────────────────────────────────────────────────────────────┐
 │  FgMDM classifier (MDM with geodesic filtering)             │
 │  Trained on source domains only                             │
 │  Target labels never used → unsupervised transductive       │
 └─────────────────────────────────────────────────────────────┘
        │  (N,)
        ▼
  Class labels — 0 or 1

Methods provided

The framework provides three methods with a unified API:

Method	Class	K	Domain adaptation	Description
MDM	MDMPipeline()	—	✗	Baseline — no alignment, FgMDM on source only
RCT	LGCRCTPipeline(half_window=0)	0	✓	Standard RCT (Zanini 2018) — no LGC
LGC-RCT	LGCRCTPipeline(half_window=10)	10	✓	Proposed method — LGC + RCT

When half_window=0, LGCRCTPipeline reduces to standard RCT with no local geometric consistency applied. Increasing K enforces stronger temporal consistency prior to domain alignment.

Evaluation protocol

The target domain participates in alignment — RCT computes its Riemannian mean from all available unlabeled covariance matrices — but no target labels are used at any stage. This constitutes an unsupervised transductive transfer learning setting (Pan & Yang, 2010). In active BCI, RCT estimates the reference matrix from resting-state periods; in passive BCI — where no rest states exist — we use all available unlabeled target windows.

Key properties

• Unsupervised transductive: no target labels required at any stage — domain alignment uses only unlabeled target data
• Standard API: follows the (X, y, domains) convention of pyriemann transfer learning
• Paradigm-agnostic: validated on mental workload and affective state classification (preliminary)

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Installation

pip install lgc-rct

For exact reproducibility of published results:

pip install -r requirements-freeze.txt
pip install lgc-rct

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Quick Start

from lgcrct import LGCRCTPipeline, MDMPipeline, run_loso

# X : np.ndarray, shape (N, C, T) — bandpass-filtered EEG windows
# y : np.ndarray, shape (N,)      — class labels {0, 1}
# domains : np.ndarray, shape (N,) — subject IDs

# MDM baseline — no domain adaptation
pipe_mdm = MDMPipeline(cov_estimator="lwf")

# RCT baseline — domain alignment, no LGC
pipe_rct = LGCRCTPipeline(half_window=0)

# LGC-RCT (proposed method — Riemannian mean, K=10)
pipe = LGCRCTPipeline(half_window=10, cov_estimator="lwf")
pipe.fit(X, y, domains, target_domain="subject_01")
y_pred = pipe.predict(X_test, y_test, domains_test)

# LGC-Euclidean ablation (arithmetic mean instead of Riemannian)
pipe_euclid = LGCRCTPipeline(half_window=10, lgc_mean="euclid")

# Full LOSO evaluation
results = run_loso(X, y, domains, half_window=10, cov_estimator="lwf")
results_euclid = run_loso(X, y, domains, half_window=10, lgc_mean="euclid")

Input format

X       : np.ndarray (N, C, T)   bandpass-filtered EEG windows
y       : np.ndarray (N,)        class labels {0, 1}
domains : np.ndarray (N,)        subject IDs (str or int)

Recommendation: apply sliding-window segmentation before calling LGC-RCT. LGC relies on temporal neighbors within each class segment — more windows per segment means richer temporal structure and stronger geometric consistency. A 4-second window with 50% overlap (2-second step) at 128 Hz is a validated configuration.

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Validated Results

Mental Workload — Team Metrics dataset (private, TNO)

34 pilots, UAV supervision task, binary workload classification, LOSO, 128 Hz.

Method	Alpha ACC	Theta ACC	No target labels?
MDM	50.56 ± 1.63	51.34 ± 2.15	—
RCT	57.74 ± 2.56	57.94 ± 3.46	YES
LGC-RCT K=1	63.11 ± 4.04	60.61 ± 3.42	YES
LGC-RCT K=10	77.73 ± 6.39	73.91 ± 6.05	YES

As reported in NAT26 Berlin proceedings.

Affective State Classification — DEAP dataset (preliminary)

32 subjects, emotion recognition, binary classification, LOSO, 128 Hz, 15–36 Hz.

Task	Method	ACC	No target labels?	Status
Valence	LGC-RCT K=10	79.52 ± 5.97	YES	preliminary
Arousal	LGC-RCT K=10	75.51 ± 5.77	YES	preliminary

These results are preliminary and obtained without any dataset-specific tuning. The method configuration (K=10, cov_estimator='lwf' (Ledoit-Wolf covariance estimator)) is identical to the one used for workload; only the frequency band differs (15–36 Hz for DEAP vs. alpha/theta for Team Metrics). They suggest that LGC-RCT generalizes across passive BCI paradigms. Full analysis forthcoming.

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Repository Structure

lgc-rct/
├── lgcrct/                                        # Installable Python package
│   ├── lgc.py                                     # LGC: block-aware local Riemannian mean on P(n)
│   ├── pipeline.py                                # LGCRCTPipeline: fit / predict / transform
│   └── evaluation.py                              # run_loso: LOSO cross-subject evaluation
├── demos/
│   └── 02_demo_deap.py                            # Demo on DEAP public dataset
├── experiments/                                   # Requires Team Metrics dataset (private, TNO)
│   ├── lgc_rct_loso.py                            # Full LOSO experiment script
│   └── lgc_ablation_deap.py                       # LGC-Riemannian vs LGC-Euclidean ablation (DEAP)
├── data/
│   └── FORMAT.md                                  # Dataset format and download instructions
└── results/
    ├── loso_34pilots_published.csv                # NAT26 Berlin — K ablation (alpha & theta)
    ├── LGC-RCT_K10_DEAP_VALENCE_15-36Hz_LOSO.csv # DEAP valence (preliminary)
    └── LGC-RCT_K10_DEAP_AROUSAL_15-36Hz_LOSO.csv # DEAP arousal (preliminary)

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Reproducibility

The LGC-RCT pipeline is fully deterministic: Ledoit-Wolf covariance estimation, Riemannian mean computation, and RCT alignment all have unique, closed-form or convergent solutions on the SPD manifold. LOSO partitioning is determined entirely by subject IDs. No random seed is required — results are exactly reproducible given the same data and dependency versions (see requirements-freeze.txt).

This property extends to third-party use: researchers who apply lgc-rct to their own datasets and publish results can guarantee exact replication by any laboratory, without dependence on random initialization, hardware, or number of runs.

Dataset availability

The Team Metrics dataset is proprietary (TNO, Netherlands) and cannot be shared. To access it for replication of the NAT26 Berlin results, contact Anne-Marie Brouwer (TNO).

The DEAP demo (demos/02_demo_deap.py) runs on the publicly available DEAP dataset. See data/FORMAT.md for download instructions.

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Dependencies

Package	Version
Python	≥ 3.9
numpy	≥ 1.26.4
pyriemann	≥ 0.9
scikit-learn	≥ 1.6.1

experiments/lgc_rct_loso.py additionally requires gumpy for EEG bandpass filtering. gumpy is not available on PyPI — install from: https://github.com/gumpy-bci/gumpy Always pass fs=128 explicitly (gumpy defaults to fs=256).

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Citation

If you use this method, please cite the paper:

@inproceedings{licona2026lgcrct,
  title     = {Local Geometric Consistency for Cross-Subject {EEG} Transfer Learning},
  author    = {Licona Mu{\~n}oz, Ricardo and
               Guetschel, Pierre and
               Bruin, Juliette and
               Yilmaz, Efecan and
               Brouwer, Anne-Marie},
  booktitle = {Proceedings of the Fifth Neuroadaptive Technology Conference (NAT'26)},
  year      = {2026},
  note      = {Berlin, Germany}
}

Paper DOI will be added upon proceedings publication.

If you use this software specifically, please also cite the software release:

@software{licona2026lgcrct_software,
  author    = {Licona Mu{\~n}oz, Ricardo and
               Guetschel, Pierre and
               Bruin, Juliette and
               Yilmaz, Efecan and
               Brouwer, Anne-Marie},
  title     = {lgc-rct: Local Geometric Consistency + Riemannian Centering Transformation},
  year      = {2026},
  publisher = {Zenodo},
  version   = {v0.2.0},
  doi       = {10.5281/zenodo.19225508}
}

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References

[1] Zanini, P., Congedo, M., Jutten, C., Said, S., & Berthoumieu, Y. (2018). Transfer Learning: A Riemannian Geometry Framework With Applications to Brain–Computer Interfaces. IEEE Transactions on Biomedical Engineering, 65(5), 1107–1116. https://doi.org/10.1109/TBME.2017.2742541

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License

MIT License — see LICENSE for details.