# Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classification

arXiv: https://arxiv.org/abs/2202.02472 · HTML: https://mlsanity.com/paper/2202.02472/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 64 references that are in the map.
- First posted on arXiv 5 Feb 2022.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [FBCNet: A Multi-view Convolutional Neural Network for Brain-Computer Interface](https://mlsanity.com/paper/2104.01233/) (2021)
- [Neural population geometry: An approach for understanding biological and artificial neural networks](https://mlsanity.com/paper/2104.07059/) (2021)
- [Deep Learning on Lie Groups for Skeleton-based Action Recognition](https://mlsanity.com/paper/1612.05877/) (2016)
- [Federated Transfer Learning for EEG Signal Classification](https://mlsanity.com/paper/2004.12321/) (2020)
- [Manifold-regression to predict from MEG/EEG brain signals without source modeling](https://mlsanity.com/paper/1906.02687/) (2019)
- [EEG-based video identification using graph signal modeling and graph convolutional neural network](https://mlsanity.com/paper/1809.04229/) (2018)
- [Analyzing Dynamical Brain Functional Connectivity As Trajectories on Space of Covariance Matrices](https://mlsanity.com/paper/1904.05449/) (2019)
- [On the interpretation of linear Riemannian tangent space model parameters in M/EEG](https://mlsanity.com/paper/2107.14398/) (2021)
- [A New Generation of Brain-Computer Interface Based on Riemannian Geometry](https://mlsanity.com/paper/1310.8115/) (2013)

## Built on by (most cited first, 21 of 21)

- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [MAtt: A Manifold Attention Network for EEG Decoding](https://mlsanity.com/paper/2210.01986/) (2022)
- [Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis](https://mlsanity.com/paper/2211.02641/) (2022)
- [Deep Riemannian Networks for End-to-End EEG Decoding](https://mlsanity.com/paper/2212.10426/) (2022)
- [Interpretable and Robust AI in EEG Systems: A Survey](https://mlsanity.com/paper/2304.10755/) (2023)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [Differential geometry with extreme eigenvalues in the positive semidefinite cone](https://mlsanity.com/paper/2304.07347/) (2023)
- [A Strong and Simple Deep Learning Baseline for BCI MI Decoding](https://mlsanity.com/paper/2309.07159/) (2023)
- [Geometric Neural Network based on Phase Space for BCI-EEG decoding](https://mlsanity.com/paper/2403.05645/) (2024)
- [Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning](https://mlsanity.com/paper/2604.20308/) (2026)
- [EEG-MACS: Manifold Attention and Confidence Stratification for EEG-based Cross-Center Brain Disease Diagnosis under Unreliable Annotations](https://mlsanity.com/paper/2405.00734/) (2024)
- [EEG-ReMinD: Enhancing Neurodegenerative EEG Decoding through Self-Supervised State Reconstruction-Primed Riemannian Dynamics](https://mlsanity.com/paper/2501.08139/) (2025)
- [HEEGNet: Hyperbolic Embeddings for EEG](https://mlsanity.com/paper/2601.03322/) (2026)
- [SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization](https://mlsanity.com/paper/2602.22895/) (2026)
- [A Human-Machine Joint Learning Framework to Boost Endogenous BCI Training](https://mlsanity.com/paper/2309.03209/) (2023)
- [NiSNN-A: Non-iterative Spiking Neural Networks with Attention with Application to Motor Imagery EEG Classification](https://mlsanity.com/paper/2312.05643/) (2023)
- [Transferring Spatial Filters via Tangent Space Alignment in Motor Imagery BCIs](https://mlsanity.com/paper/2504.17111/) (2025)
- [NeuroPhysNet: A FitzHugh-Nagumo-Based Physics-Informed Neural Network Framework for Electroencephalograph (EEG) Analysis and Motor Imagery Classification](https://mlsanity.com/paper/2506.13222/) (2025)
- [RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs](https://mlsanity.com/paper/2602.22981/) (2026)
- [MPNet: A Robust and Efficient Manifold Pooling Network for Multi-Rhythm EEG Signal Decoding](https://mlsanity.com/paper/2605.05212/) (2026)
- [MGMCL: Multi-Granularity Manifold Contrastive Learning With Neural ODEs for Cross-Subject EEG Emotion Recognition](https://mlsanity.com/paper/2608.08440/) (2026)

## Abstract (arXiv)

Deep learning (DL) has been widely investigated in a vast majority of applications in electroencephalography (EEG)-based brain-computer interfaces (BCIs), especially for motor imagery (MI) classification in the past five years. The mainstream DL methodology for the MI-EEG classification exploits the temporospatial patterns of EEG signals using convolutional neural networks (CNNs), which have remarkably succeeded in visual images. However, since the statistical characteristics of visual images depart radically from EEG signals, a natural question arises whether an alternative network architecture exists apart from CNNs. To address this question, we propose a novel geometric deep learning (GDL) framework called Tensor-CSPNet, which characterizes spatial covariance matrices derived from EEG signals on symmetric positive definite (SPD) manifolds and fully captures the temporospatiofrequency patterns using existing deep neural networks on SPD manifolds, integrating with experiences from many successful MI-EEG classifiers to optimize the framework. In the experiments, Tensor-CSPNet attains or slightly outperforms the current state-of-the-art performance on the cross-validation and holdout scenarios in two commonly-used MI-EEG datasets. Moreover, the visualization and interpretability analyses also exhibit the validity of Tensor-CSPNet for the MI-EEG classification. To conclude, in this study, we provide a feasible answer to the question by generalizing the DL methodologies on SPD manifolds, which indicates the start of a specific GDL methodology for the MI-EEG classification.