Systematic Evaluation of Euclidean Alignment with Deep Learning for EEG Decoding

Background Introduction

Electroencephalogram (EEG) signals are widely used in brain-computer interface (BCI) tasks due to their non-invasive nature, portability, and low acquisition cost. However, EEG signals suffer from low signal-to-noise ratio, sensitivity to electrode positioning, and poor spatial resolution. With the advancement of deep learning (DL) techniques, they have shown outstanding performance in the BCI field, even outperforming traditional machine learning methods in some cases. However, the high data demand of DL models remains a major obstacle. Transfer Learning (TL) with multi-subject data can more efficiently train DL models by sharing data. Euclidean Alignment (EA) has gained attention due to its ease of use, low computational complexity, and compatibility with DL models. But existing research has limited evaluation of the training performance of EA combined with DL for global and individual models. This paper aims to systematically evaluate the impact of EA and DL combination on the training performance for BCI signal decoding.

Paper Source and Author Information

This paper is titled “Systematic Evaluation of Euclidean Alignment with Deep Learning for EEG Decoding” and is written by Bruna Junqueira, Bruno Aristimunha, Sylvain Chevallier, and Raphael Y. De Camargo. The authors are respectively from the University of São Paulo, Université Paris-Saclay (Inria TAU Team, LISN-CNRS), and the Federal University of ABC. The paper is published in an academic journal, and the corresponding author is Bruna Junqueira (brunaafl@usp.br).

Research Methods

EEG Decoding Framework

EEG decoding is a significant problem in BCI, i.e., how to classify mental states from recorded signals. The dataset E consists of n pairs of experiments and labels (x_i, y_i). The experiment recording X is a c-by-t matrix, where c is the number of channels and t is the number of time steps. The feature space is X ∈ R^c×t. This experiment focuses solely on the left-right imagery paradigm, and the classification label space is {‘left_hand’, ‘right_hand’}.

Considering the variability of brain signals, it is assumed that the marginal distributions p_k(·) from different subjects are different. The classification hypothesis assumes an unknown decision function fθ(·) whose parameters θ satisfy fθ(x) = y. By inputting labeled data into a neural network and minimizing the average loss ℓ:

[ \min_θ \frac{1}{nt} \sum{i=1}^{n_t} ℓ(fθ(x_i), y_i) ]

All experiments in this paper use negative log-likelihood loss and the AdamW optimizer.

Transfer Learning Framework

A domain d is defined by the feature space X and the marginal distribution p(x), and a task t is defined by the label set Y and the decision function f(X). In this paper, each individual is regarded as a domain, the source domain is the known knowledge domain, and the target domain is the unknown domain. The transfer learning framework trains a model on the source domain (D_s) and source task (T_s), and applies it to the target domain (D_t) and target task (T_t).

Euclidean Alignment

Euclidean Alignment (EA) reduces the differences between subjects by matching the covariance matrix of all experiments for each subject with the identity matrix. Assuming there are n experiments for each of the n subjects, the covariance matrix is defined as:

[ R̄j = \frac{1}{n} \sum{i=1}^{n} X_j_i X^T_j_i ]

The transformation matrix is defined as the inverse square root of R̄j and is applied to each experiment.

Datasets

Two datasets are used in this paper: Dataset IIA (BNCI2014) from the BCI Competition 4 and Schirrmeister2017 (high gamma). BNCI2014 includes data from 9 healthy individuals, each performing four motor imagery tasks: left hand, right hand, both feet, and tongue. The high gamma dataset includes data from 14 healthy individuals performing left hand, right hand, both feet, and rest tasks. Only left and right hand data are used to maintain consistency in the results. Standard pre-processing steps include band-pass filtering and resampling.

Models and Data Splitting

The paper analyzes the application of EA in two scenarios:

1. Using data from all source subjects (cross-subject model).
2. Using data from each source subject individually (individual model).

A two-class classification task with the motor imagery paradigm is used for evaluation on the target subject’s two-class task to prevent data leakage between test, validation, and training sets.

EEGNet, ShallowNet, and DeepNet are used as evaluation models to ensure a fair comparison.

Data Alignment

In offline and pseudo-online experiments, different methods are used for EEG alignment. In offline experiments, all experiments for each subject are aligned. In the pseudo-online case, only the first 24 experiment blocks from the target subject are used to calculate the reference matrix and align the test data.

Model Training

The cross-subject model uses a leave-one-subject-out split, and the individual model uses all data for training, with 20% used for validation. A separate model is trained for each target subject, evaluating a many-to-many training scenario. During training, the batch size is 64, with 1000 epochs, early stopping at 250, 25% dropout rate, and tuning of the learning rate and weight decay parameters.

Research Results

Euclidean Alignment in Transfer Learning

Euclidean Alignment improved decoding performance across all evaluated datasets and architectures. The offline-EA method trained on data from all subjects improved accuracy by 1.26% compared to the motor imagery paradigm, while online-EA improved overall accuracy by 4.33% compared to the unaligned case, overall reducing training time by approximately 70%.

Impact of Fine-Tuning on Shared Models

Fine-tuning on the unaligned pipeline showed an average accuracy improvement of 1.43%. Fine-tuning on top of the offline-EA and online-EA accuracies did not result in significant changes, suggesting that EA has already made the data distributions highly consistent, and in this case, fine-tuning requires more target data.

Analysis of Inter-Subject Transferability

Euclidean Alignment improved the inter-subject transferability accuracy of individual models. Good donors typically performed well as receivers, and EA increased this association, making the data distributions more consistent. However, EA did not change the structure of good and bad donors.

Application of Voting Classifiers in Transfer Learning

EA significantly improved the transferability of individual models. By using a weighted majority voting classifier to classify the target subject, using different combinations of individual models, EA improved the average accuracy by 3.71%. Compared to the shared model, there was a 3.62% reduction in overall average accuracy. However, the voting classifier construction is more flexible, allowing the addition of new data sources without retraining the entire model.

Significance and Value

This paper demonstrates Euclidean Alignment as a powerful domain adaptation technique, performing exceptionally when combined with DL. EA significantly improved the decoding accuracy and training time of models with multi-subject data. When training cross-subject models, EA should be used as a standard pre-processing step. Future research could further explore the fast convergence issue of EA in deep learning models and the impact of different hyperparameters on model performance to achieve broader application prospects.

By systematically evaluating the application of EA combined with DL in EEG decoding, not only has it advanced the technology in the BCI field, but it has also opened up new directions for further research. The study reveals the potential of EA in reducing inter-subject signal variability, providing a more effective transfer learning approach, and offering important guidance for the practical application of BCI technology.