This paper provides a comprehensive review of classification algorithms used in Brain-Computer Interface (BCI) systems based on Electroencephalography (EEG). The authors, Fabien Lotte, Marco Congedo, Anatole Lécuyer, Fabrice Lamarche, and Bruno Arnaldi, from IRISA/INRIA Rennes and France Telecom R&D, discuss the critical properties of commonly employed algorithms and compare their performance. The paper aims to provide guidelines for selecting the most suitable classification algorithm for specific BCI experiments. The review covers five main categories of classifiers: linear classifiers (e.g., Linear Discriminant Analysis, SVM), neural networks (e.g., MultiLayer Perceptron), nonlinear Bayesian classifiers (e.g., Bayes quadratic, Hidden Markov Model), nearest neighbor classifiers (e.g., k-Nearest Neighbors, Mahalanobis distance), and combinations of classifiers (e.g., boosting, voting, stacking). Key points discussed include: - **Feature Extraction**: The importance of considering time variations in EEG signals and the challenges posed by noise, high dimensionality, and non-stationarity. - **Classification Algorithms**: Taxonomy, properties, and performance in BCI applications, with a focus on the curse-of-dimensionality and the Bias-Variance tradeoff. - **Synchronous vs. Asynchronous BCI**: SVMs, dynamic classifiers, and combinations of classifiers are particularly effective for synchronous BCI, while dynamic classifiers do not show significant advantages over static classifiers in asynchronous BCI. - **Feature Properties**: Regularized classifiers like SVMs are better suited for noisy and high-dimensional data, while simple classifiers like LDA are more robust for small training sets. The paper concludes by providing guidelines for choosing the appropriate classifier based on the type of BCI and the specific characteristics of the features used. It also highlights the potential of combining classifiers to reduce variance and improve performance.This paper provides a comprehensive review of classification algorithms used in Brain-Computer Interface (BCI) systems based on Electroencephalography (EEG). The authors, Fabien Lotte, Marco Congedo, Anatole Lécuyer, Fabrice Lamarche, and Bruno Arnaldi, from IRISA/INRIA Rennes and France Telecom R&D, discuss the critical properties of commonly employed algorithms and compare their performance. The paper aims to provide guidelines for selecting the most suitable classification algorithm for specific BCI experiments. The review covers five main categories of classifiers: linear classifiers (e.g., Linear Discriminant Analysis, SVM), neural networks (e.g., MultiLayer Perceptron), nonlinear Bayesian classifiers (e.g., Bayes quadratic, Hidden Markov Model), nearest neighbor classifiers (e.g., k-Nearest Neighbors, Mahalanobis distance), and combinations of classifiers (e.g., boosting, voting, stacking). Key points discussed include: - **Feature Extraction**: The importance of considering time variations in EEG signals and the challenges posed by noise, high dimensionality, and non-stationarity. - **Classification Algorithms**: Taxonomy, properties, and performance in BCI applications, with a focus on the curse-of-dimensionality and the Bias-Variance tradeoff. - **Synchronous vs. Asynchronous BCI**: SVMs, dynamic classifiers, and combinations of classifiers are particularly effective for synchronous BCI, while dynamic classifiers do not show significant advantages over static classifiers in asynchronous BCI. - **Feature Properties**: Regularized classifiers like SVMs are better suited for noisy and high-dimensional data, while simple classifiers like LDA are more robust for small training sets. The paper concludes by providing guidelines for choosing the appropriate classifier based on the type of BCI and the specific characteristics of the features used. It also highlights the potential of combining classifiers to reduce variance and improve performance.