Applied Examples

Real-world applications demonstrating SPD Learn models on EEG, fMRI, and other neuroimaging data. These examples show how to use pre-built architectures for practical machine learning tasks.

Tutorials

Step-by-step tutorials for getting started with SPD Learn. Start here to learn the fundamentals of SPD matrices, neural network building blocks, and complete classification pipelines.

Batch Normalization on SPD Manifolds

Batch Normalization on SPD Manifolds

End-to-End EEG Classification Tutorial

End-to-End EEG Classification Tutorial

Understanding Symmetric Positive Definite (SPD) Matrices

Understanding Symmetric Positive Definite (SPD) Matrices

Building Blocks of SPD Neural Networks

Building Blocks of SPD Neural Networks

Numerical Precision and Stability for SPD Networks

Numerical Precision and Stability for SPD Networks

How-to Guides

Task-oriented guides for solving specific problems with SPD Learn. Each guide addresses one focused question and assumes you already understand the basics (see Tutorials if you’re just getting started).

How to Add Batch Normalization to an SPDNet

How to Add Batch Normalization to an SPDNet

How to Choose a Metric for Batch Normalization

How to Choose a Metric for Batch Normalization

SPD Layer Visualizations

These animated visualizations help understand how each SPD neural network layer transforms data on the Riemannian manifold. Each animation shows the geometric operation performed by the layer using 2x2 SPD matrices visualized as ellipsoids.

LogEig: Linearization and the Swelling Effect

LogEig: Linearization and the Swelling Effect

BiMap Layer Animation

BiMap Layer Animation

ReEig Layer Animation

ReEig Layer Animation

SPD Batch Normalization Animation

SPD Batch Normalization Animation

CovLayer Animation

CovLayer Animation

Applied Examples

Examples demonstrating analysis of EEG, fMRI and how to use each model in spd_learn.

Manifold Attention with MAtt

Manifold Attention with MAtt

Testing Robustness of SPD Models with Riemannian PGD Attack

Testing Robustness of SPD Models with Riemannian PGD Attack

Classifying fMRI data with SPDNet

Classifying fMRI data with SPDNet

EEG Classification with EEGSPDNet

EEG Classification with EEGSPDNet

Learnable Wavelets with GREEN for EEG Classification

Learnable Wavelets with GREEN for EEG Classification

Phase-Space Embedding with PhaseSPDNet

Phase-Space Embedding with PhaseSPDNet

Filter Bank Motor Imagery with TensorCSPNet

Filter Bank Motor Imagery with TensorCSPNet

Parallel Transport on SPD Manifolds

Parallel Transport on SPD Manifolds

SPDIM: Source-Free Domain Adaptation on SPD Manifolds

SPDIM: Source-Free Domain Adaptation on SPD Manifolds

Radar Image Classification with SPD Learn

Radar Image Classification with SPD Learn

Cross-Session Transfer with TSMNet

Cross-Session Transfer with TSMNet

Reproducing LieBN Paper Results (Table 4)

Reproducing LieBN Paper Results (Table 4)

Benchmarking SPD Learn Models with MOABB and Hydra

Benchmarking SPD Learn Models with MOABB and Hydra