###### Abstract  
Canonical correlation analysis (CCA) has been used for the steady-state visual evoked potential (SSVEP) based brain-computer interface (BCI) for a long time. However, the reference signal of CCA is relatively simple and lacks subject-specific information. Moreover, over-fitting may occur when a short time window (TW) length was used in CCA. In this article, an optimized L1-regularized multiway canonical correlation analysis (L1-MCCA) is combined with a support vector machine (SVM) to overcome the aforementioned shortcomings in CCA. The correlation coefficients obtained by L1-MCCA were transferred into a particle-swarm-optimization (PSO)-optimized support vector machine (SVM) classifier to improve the classification accuracy. The performance of the proposed method was evaluated and compared with the traditional CCA and power spectral density (PSD) methods. The results showed that the accuracy of the L1-MCCA-PSO-SVM was 96.36% and 98.18% respectively when the TW lengths were 2 s and 6 s. This accuracy is higher than that of the traditional CCA and PSD methods. steady-state visual evoked potential (SSVEP); brain-computer interface (BCI); l1-regularized multiway canonical correlation analysis (L1-MCCA); support vector machine (SVM); particle swarm optimization (PSO) +
Footnote †: journal: Applied  
flashing at 5-30 Hz [19]. The neural responses acquired by EEG have peak frequencies that are the fundamental and harmonic frequencies of the flicker frequency. Therefore, the user's target can be identified by matching the characteristics of the acquired EEG signals to the command-related particular flicker frequency. The power spectral density (PSD) method was one of the earliest methods applied to SSVEP. Since SSVEP itself carries the frequency characteristics of visual stimuli, the frequency components corresponding to the stimulation frequency can be used as the characteristic values [20,21]. However, the PSD approach has some drawbacks, such as sensitivity to noise, low signal-to-noise ratio, and requirement of a relatively long time window (TW) if higher accuracy is needed [22,23]. To overcome these problems, several techniques have been proposed in the past few years. Canonical correlation analysis (CCA) proposed by [PERSON] et al. [24], analyzes SSVEP signals by studying the linear relationship between two sets of multidimensional vectors. CCA combined with multiway EEG data improves the signal-to-noise ratio. It has been found that CCA could achieve a higher classification accuracy than the PSD with a shorter TW [25,26]. In recent years, the studies based on CCA have provided valuable information in the field of BCI research. However, the reference signal of CCA is only composed of standard sine and cosine signals. It lacks subject-specific information about the neural responses of the brain [27,28]. To further improve the performance of BCI systems, multiway canonical correlation analysis (MCCA) based on tensor analysis was proposed. Specifically, MCCA constructs an EEG tensor from the multiway EEG signals recorded by multiple experiments and alternately learns the projection vector used for reference signal optimization from the channel array of the EEG tensor and the test channel array. Based on tensor analysis [29] and sparse regularization, [PERSON] et al. [30] have proposed the L1-regularized multiway canonical correlation analysis (L1-MCCA). L1 regularization [31,32,33] was used to further strengthen MCCA's test channel array optimization so that L1-MCCA has the best projection vector effect when learning reference signal optimization. During the data training process, the L1-MCCA has the stronger ability to learn projection vectors and prevent signal overfitting. SVM is suitable for small-sample classification problems, has no limitation on data dimension, and has good generalization ability and robustness, and can learn multiple relations [34,35]. Inputting the correlation coefficient matrix obtained by L1-MCCA into SVM for classification may achieve better performance.