## 2 Materials and Methods
### Feature Classification  
TCN is a simple but powerful CNN sequence processing architecture that integrates several CNN techniques [20]. First, as shown in Figure 4, TCN used causal convolution to prevent information leakage from the future into the past, and thus it was necessary to calculate the output for the current time point by only using the features before that time point. Therefore, causal convolution was different from the conventional convolution methods and it could allow real-time processing in a similar manner to LSTM. However, the TCN outputs were only related to the inputs and they were not based on the previous outputs, so TCN differed from LSTM because LSTM was necessary to wait for the predecessor results to obtain the current outputs. Thus, TCN had the advantage of parallel operation.  
Second, TCN employed dilated convolution [22], as shown in Figure 5. For a filter \(f=[W0\ \cdots\ Wi]\) for \(i=0\),..., \(M\)\(-\)1 and the complete input feature sequence \(\mathbf{Z}(t)\), the formula for the dilated convolution operation \(F\) is as follows [20],  
\[\mathbf{F}(s)=(\mathbf{Z}*_{d}f)(s)=\sum_{i=0}^{M-1}\mathbf{f}(i)\cdot\mathbf{Z_{s-d}i} \tag{2}\]  
where \(d\) is the dilation factor, \(M\) is the filter size, and \(s-d\)\(i\) denotes the positions of the features that need to be calculated in the past. \(d\) determines the number of interval time points between every two adjacent filter taps. When \(d=1\), a dilated convolution became a conventional convolution. The receptive field could be expanded rapidly by increasing the factor \(d\) for dilated convolution in a layer by layer manner. The receptive field could be roughly understood as the length needed for the input features for each  
Figure 4: Simplified visualization of causal convolution and conventional convolution.  
output. In general, compared with conventional CNN, TCN using dilated convolution greatly reduced the amount of calculations required when the receptive field is the same size.  
Third, each TCN layer used residual connections [23], which were calculated with the following formula,  
\[O=\textit{Activation}(x+\mathbf{F}(x)) \tag{3}\]  
The residual structure allowed the results from each layer to be merged into the final layer, and thus each layer could be effectively learned. The extensive use of residual structures in deep learning also demonstrated the benefit of this structure. TCN employed a generic residual module instead of a convolutional layer to improve the stabilization of the deep network, as shown in Figure 6.  
In addition, as shown in Figure 7, TCN could increase the depth of the network by increasing the number of stacks, and thus the receptive field expands rapidly. As mentioned above, the scale of the receptive field could be roughly regarded as the product of the number of residual blocks, kernel size, and the last dilation factor d. RNN could also synthesize long-distance information but it could not accurately control the actual time length of the integrated information in the same manner as TCN [20].  
After calculating the features with TCN, we connected a Softmax layer to output four values at each time point as the probabilities of the four states, and the feature classification results were actually the probabilities. In particular, the direct classification results or annotations were obtained according to the state where the corresponding probability was the maximum of the four probabilities at each time point. Thus, direct classification results could determine the classification performance of the  
Figure 5: Simplified visualization of a TCN with kernel = 2, stack = 1, and dilation structure = [1, 2, 4].  
Figure 6: Residual block.  
feature classification algorithms. In the experimental section, we present comparisons of different classification algorithms.