## 4 Discussion  
In the past few years, several studies have been proposed for improving the classification performance of the SSVEP-based BCI. SSVEP analysis method has been gradually shifted from one-way optimization to collaborative multiway optimization. Moreover, discriminant analysis of regularized tensors has begun to appear and was applied to classifiers to prevent overfitting. In this study, an approach that combines L1-MCCA with PSO-optimized SVM was proposed. The performance of L1-MCCA was compared quantitatively with CCA and PSD before and after PSO-SVM optimization. Note that the classification accuracies of the L1-MCCA related methods with varied TWs were consistently higher than the CCA-related and PSD-related methods. Our results are in agreement with previous research [30; 41; 42]. It has been reported that the L1-MCCA method can improve the classification accuracy of SSVEP-based BCI by optimizing the reference signal. As shown in Figure 4, the correlation coefficients corresponding to the disparate stimulation frequencies for both L1-MCCA and CCA were calculated. The results showed that compared with CCA, L1-MCCA improves the correlation coefficient of the target frequency and reduces the correlation coefficient of other non-target frequencies, indicating the effectiveness of L1-MCCA in SSVEP classification. The key to achieving a better classification performance is to separate the target frequency from other non-target frequencies more accurately. The greater differences in the correlation coefficients between the two, the better the classification performance. The results showed that the combination of multiway analysis and regularization allowed L1-MCCA to present better performance than that of the traditional CCA method. The length of the TW has a significant influence on the classification accuracy of SSVEP-based BCI. As shown in Figures 3 and 4, the classification accuracies were gradually increased as the length of the TW increased. In this study, nine visual stimulations with different frequencies were used to produce the SSVEP data. The accuracy of the CCA of the 4 s TW was 88.58%. [PERSON] et al. [43] reported that under the CCA-based method, the average accuracy of 10 subjects with 4 s TW for 12 stimuli reached about 93%, which was higher than the accuracy of this study. [PERSON] et al. [44] reported that under the four stimuli, the CCA-based method had reached 62% accuracy with a 4 s TW for nine subjects. The effect of TW on the classification of the current study is in agreement with these previous studies. The longer the TW, the more experimental information obtained, and the higher the classification accuracy. The reasons why the classification accuracies of different studies are different from each other can be ascribed into several factors, such as the differences in experimental design, individual, data processing method, and individual difference, etc. Different from the traditional CCA which uses the standard sine and cosine waves as reference signals, the L1-MCCA method optimizes reference signals with subject-specific information to obtain a better performance. The results of the current study are in line with the study proposed by [PERSON] et al. [30]. The average accuracy of L1-MCCA obtained by 10 subjects with 4 s TW, which is about 91%, was higher than that of MCCA and CCA, showing the effectiveness of L1-MCCA in SSVEP-based BCI. In this study, due to the unique advantages of PSO, such as fast convergence speed and simple calculation, the SVM classifier which is optimized by PSO combined with L1-MCCA was used, aiming at the further improvement of the classification accuracy. To test the feasibility and evaluate the performance of the proposed algorithm, quantitative comparisons were conducted for inconsistent methods in terms of classification accuracy. As shown in Figure 5, at the same TW, the accuracy of the L1-MCCA was higher than that of the CCA and PSD.