## 3 Results and Discussion
### The Results Compared with Other Approaches  
In this section, the statistical approaches including canonical correlation analysis (CCA), filter bank CCA (FBCCA), and task-related component analysis (TRCA) [21] and the neural network approaches including EEGNet [31] and MTL [29] were selected for comparison with the proposed approaches. For EEGNet, we designed two neural network structures, which differ in that the second convolutional block is either a traditional convolutional operation (referred to as EEGNet_1) or a convolutional operation across the channel dimension (referred to as EEGNet_2). The experimental results for both the statistical and neural network approaches are shown in Figure 3. Our findings indicate that the convolutional operation across the channel dimension, as used in EEGNet_2, can effectively fuse information from different channels and obtain more precise embedding features for representing the input SSVEP signal. Furthermore, our proposed approach, MDF, outperforms the selected neural network-based approaches. If the input SSVEP signal has a short duration, the SSVEP-based BCI can offer a quick response time and can be used to develop real-time systems. In Figure 3, neural network-based approaches outperform statistical approaches when the duration of the input SSVEP signal is 1 s. Moreover, the proposed MDF approach achieves the best performance, making it an excellent option for practical applications. A statistical analysis typically requires a longer duration for the input SSVEP signal to achieve acceptable performance. As such, the duration of an input SSVEP signal should be larger than 3 s. However, this is not suitable for developing a real-time system and may be unacceptable for users. Therefore, it is crucial for neural network-based approaches to increase the precision of representing an SSVEP signal with a long duration. Researchers may employ multi-task learning with non-classification tasks to extract meaningful embedding features, potentially leading to improved performance. \begin{table}
\begin{tabular}{c c c c c} \hline  & **4 s** & **3 s** & **2 s** & **1 s** \\ \hline \multirow{2}{*}{TDF} & MDF1 & 24.2 & 40.6 & 43.5 & 9.4 \\  & MDF2 & 25.8 & 41.7 & 44.3 & 10.0 \\ \hline \multirow{2}{*}{FDF} & MDF1 & 31.5 & 26.9 & 31.5 & 35.3 \\  & MDF2 & 32.9 & 28.2 & 32.4 & 35.8 \\ \hline \end{tabular}
\end{table} 
Table 5: The improvement rate (%) for MDF1 and MDF2 comparing with that using time- and frequency-domain features (TDF: time-domain feature, FDF: frequency-domain feature). Finally, the proposed approach was compared with state-of-the-art neural networks, including a transformer-based deep neural network model (denoted as SSVEPformer) [18] and a group depth-wise convolutional neural network (denoted as GDNet-EEG) [19]. The duration of the input SSVEP signal for SSVEPformer and GDNet-EEG is 1 s. The accuracies for SSVEPformer and GDNet-EEG are 83.16% and 84.11%, respectively, while their corresponding information transfer rates (ITR) [18] are 151.11 bits/min and 154.02 bits/min. Our proposed approach achieves an accuracy of 85.6% and an ITR of 158.65 bits/min, outperforming both SSVEPformer and GDNet-EEG. These results highlight the effectiveness of our model, particularly in improving ITR, which is crucial for real-world BCI applications. Comparing the performance of statistical approaches and neural network-based approaches, the proposed neural network-based method outperforms statistical approaches for short-duration signals but performs comparably or slightly worse for longer durations. Traditional statistical approaches like CCA and FBCCA leverage the periodicity of SSVEPs to enhance the signal-to-noise ratio (SNR). As the signal duration increases, these methods benefit from a larger amount of accumulated data, allowing them to improve the frequency detection and suppress noise more effectively. Conversely, neural networks extract discriminative features from shorter temporal windows and may not fully capitalize on the increased signal length.