pydmdeeg

Dynamic Mode Decomposition for EEG Signal Analysis

A Python library for extracting spatio-temporal coherent patterns from EEG data using Dynamic Mode Decomposition (DMD). This method enables data-driven decomposition of neural recordings into interpretable oscillatory modes.

Features

• Two DMD algorithms: Exact and standard implementations based on Tu et al. (2014)
• Sliding window analysis: Configurable window size and overlap for time-resolved decomposition
• Delay embedding: Shift-stacking technique for enhanced temporal dynamics capture
• SVD truncation: Optional hard thresholding (optht) or fixed-rank truncation for noise reduction
• Data scaling: Multiple preprocessing options (centering, normalization, z-scoring)
• Rich visualization: Built-in plotting for DMD spectra, channel statistics, and reconstruction errors
• Multi-trial support: Handle epoched EEG data with trial labels for condition comparisons

Installation

From PyPI (recommended)

pip install pydmdeeg

From source

git clone https://github.com/christiangoelz/pydmdeeg.git
cd pydmdeeg
pip install -e ".[dev]"

Quick Start

import numpy as np
from pydmdeeg import DMD

# Generate synthetic EEG-like data
# Shape: (n_trials, n_channels, n_timepoints)
n_trials, n_channels, n_times = 10, 64, 1000
sampling_rate = 256  # Hz

# Create data with oscillatory components
t = np.linspace(0, n_times/sampling_rate, n_times)
X = np.zeros((n_trials, n_channels, n_times))
for trial in range(n_trials):
    for ch in range(n_channels):
        # Alpha (10 Hz) and beta (20 Hz) oscillations with noise
        X[trial, ch, :] = (
            np.sin(2 * np.pi * 10 * t) +
            0.5 * np.sin(2 * np.pi * 20 * t) +
            0.3 * np.random.randn(n_times)
        )

# Trial labels (e.g., 0 = rest, 1 = task)
y = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1, 1])

# Channel names
channels = [f'Ch{i+1}' for i in range(n_channels)]

# Initialize DMD
dmd = DMD(
    X=X,
    y=y,
    channels=channels,
    dt=1/sampling_rate,
    win_size=128,
    overlap=64,
    algorithm='exact',
    datascale='norm'
)

# Run decomposition
dmd.DMD_win()

# Extract alpha band (8-12 Hz) mode statistics
alpha_stats = dmd.mode_stats(fbands=[[8, 12]], labels=[0, 1])
print(alpha_stats)

# Get mode magnitudes for specific frequency band
psi = dmd.get_PSI(fband=[8, 12], labels=[1])

API Reference

DMD Class

DMD(
    X,                    # EEG data: (n_trials, n_channels, n_times) or (n_channels, n_times)
    y,                    # Trial labels: (n_trials,)
    channels,             # Channel names: list of strings
    dt,                   # Sampling interval: 1/sampling_rate
    stacking_factor=0,    # Delay embedding factor (0 = no stacking)
    win_size=100,         # Window size in samples
    overlap=0,            # Window overlap in samples
    datascale='norm',     # Scaling: 'none', 'centre', 'norm', 'centre_norm'
    algorithm='exact',    # DMD algorithm: 'exact' or 'standard'
    truncation={'method': None, 'keep': None}  # SVD truncation settings
)

Key Methods

Mathematical Background

Dynamic Mode Decomposition approximates the linear operator A that best maps consecutive time snapshots:

X' ≈ AX

where X and X' are time-shifted data matrices. The eigenvalues of A (λ) encode oscillation frequencies and growth/decay rates, while eigenvectors (Φ) represent spatial patterns.

For EEG analysis:

• Frequencies: μ = Im(log(λ)) / (2πΔt)
• Spatial modes: Φ shows channel contributions to each oscillatory pattern
• Amplitudes: |Φ| weighted by initial conditions

Publications Using This Method

This implementation has been validated in peer-reviewed neuroscience research:

1. Goelz C et al. (2021). Classification of visuomotor tasks based on electroencephalographic data depends on age-related differences in brain activity patterns. Neural Networks. DOI

2. Goelz C et al. (2021). Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults. Cognitive Neurodynamics. DOI

3. Goelz C et al. (2018). Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics. Frontiers in Physiology. DOI

4. Vieluf S et al. (2018). Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control. Neuroscience. DOI

References

• Brunton BW et al. (2016). Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition. J Neurosci Methods. DOI
• Tu JH et al. (2014). On dynamic mode decomposition: Theory and applications. J Computational Dynamics. DOI
• Donoho D & Gavish M (2014). The Optimal Hard Threshold for Singular Values is 4/√3. IEEE Trans Information Theory. DOI

Contributing

Contributions are welcome! Please see CONTRIBUTING.md for guidelines.

# Install development dependencies
pip install -e ".[dev]"

# Run tests
pytest

# Run linting
ruff check .

# Run type checking
mypy pydmdeeg

License

MIT License - see LICENSE for details.

Citation

If you use this software in your research, please cite:

@software{pydmdeeg,
  author = {Goelz, Christian},
  title = {pydmdeeg: Dynamic Mode Decomposition for EEG Analysis},
  url = {https://github.com/christiangoelz/pydmdeeg},
  version = {0.2.0},
  year = {2024}
}