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Common spatial pattern (CSP) is a classic method commonly used in multichannel electroencephalogram (EEG) signal processing, which aims to extract effective features for binary classification by solving spatial filters that maximize the ratio of filtered dispersion between two classes. The aim of this paper is to improve the performance of the conventional CSP method, which will be badly influenced by noises. The recently proposed quantized minimum error entropy (QMEE) criterion is applied to structure a new objective function instead of the ${L} _{2}$ -norm in the conventional CSP. Quantization is utilized to reduce the computational complexity. The new objective function is optimized by a gradient-based iterative algorithm. The desirable performance of the QMEE-based CSP method, namely CSP-QMEE, is demonstrated with a toy example and two real EEG datasets, including Dataset IIb of the brain–computer interfaces (BCIs) Competition IV (three channels) and Dataset IIIa of the BCI Competition III (60 channels). The new method can achieve satisfactory performance compared to existing methods on all datasets. The promising results in this paper suggest that the CSP-QMEE may become a powerful tool for BCIs. [ABSTRACT FROM AUTHOR]

Minimum error entropy with fiducial points (MEEF) has received a lot of attention, due to its outstanding performance to curb the negative influence caused by non-Gaussian noises in the fields of machine learning and signal processing. However, the estimate of the information potential of MEEF involves a double summation operator based on all available error samples, which can result in large computational burden in many practical scenarios. In this paper, an efficient quantization method is therefore adopted to represent the primary set of error samples with a smaller subset, generating a quantized MEEF (QMEEF). Some basic properties of QMEEF are presented and proved from theoretical perspectives. In addition, we have applied this new criterion to train a class of linear-in-parameters models, including the commonly used linear regression model, random vector functional link network, and broad learning system as special cases. Experimental results on various datasets are reported to demonstrate the desirable performance of the proposed methods to perform regression tasks with contaminated data. [ABSTRACT FROM AUTHOR]

The minimum error entropy (MEE) criterion has been receiving increasing attention due to its promising perspectives for applications in signal processing and machine learning. In the context of Bayesian estimation, the MEE criterion is concerned with the estimation of a certain random variable based on another random variable, so that the error's entropy is minimized. Several theoretical results on this topic have been reported. In this work, we present some further results on the MEE estimation. The contributions are twofold: (1) we extend a recent result on the minimum entropy of a mixture of unimodal and symmetric distributions to a more general case, and prove that if the conditional distributions are generalized uniformly dominated (GUD), the dominant alignment will be the MEE estimator; (2) we show by examples that the MEE estimator (not limited to singular cases) may be non-unique even if the error distribution is restricted to zero-mean (unbiased). [ABSTRACT FROM AUTHOR]