# Few-Shot Continuous Authentication for Mobile-Based Biometrics
## 3 Method
### Local Feature Pooling-Based Temporal Convolution Network (LFP-TCN)  
The TCN is a CNN variant for sequential data modeling [30]. The characteristics of TCN are manifested by causal convolution and dilated convolution. In Figure 2, the blue lines illustrate convolutional filters by the dilated causal convolution with the kernel size of 3. The causal convolution is performed on elements only at the same and earlier time steps in the previous layer. This is achieved by the causal padding, i.e., adding zero-padding of length of (kernel size \(\times\) dilation rate \(-1\)) in front of inputs. Additionally, the dilated convolution is performed on non-successive elements with a fixed step (dilation rate), which efficiently enlarges the receptive field. These characteristics enable the TCN to learn relationships of very long sequences effectively. On the other hand, the dilated convolution fails to aggregate local feature information neighboring elements have [34; 35]. This is because the dilated convolution kernel is spatially discrete. In image segmentation, this problem hinders the learning of small objects. [PERSON] et al. addressed it by adding the local feature extraction (LFE) module, composed of convolutional layers with decreasing dilation rates along with the depth of layers [34]. [PERSON] et al. proposed the concentrated-comprehensive convolution, in which two depth-wise convolutions are performed before the dilated convolution [35]. The local information loss also occurs in the TCN. For example, in Figure 2, the output at the last time step \(\hat{x}_{T}\) is affected by the elements connected with blue lines. We can observe that every detail is connected between layers when the dilation rate is one. In contrast, the connection becomes more sparse as the dilation rate increases, and many hidden layer elements are completely non-connected. This means that more feature information is lost in higher layers, and only specific global features are aggregated at the output layer. Note that classifiers for time series are based on the many-to-one architecture, classifying inputs based on the output only at the last time step. This issue forces the TCN to focus on specific global information and prevents learning refined representations of touch-gestures. However, for this problem, the existing methods [34; 35] are not preferable in mobile-based biometrics because using additional convolution layers increases model complexity. Figure 2: Convolution by the LFP-TCN: The convolution is performed with the kernel size of 3 and dilation rate of \((1,2,4)\). The colored elements in hidden layers illustrate max-pooled elements. The kernel size of the max-pooling is the same as the dilation rate on each layer. This operation compresses local information of neighboring non-filtered elements. Considering the limited memory capacity of mobile devices, we designed the LFP module, a parameter-free method to prevent local information loss. Specifically, the LFP module extracts salient feature information from neighboring elements with max-pooling before the dilated convolution is performed. Figure 2 illustrates the convolution by the LFP-TCN. The LFP module performs the causal padding and max-pooling to inputs of convolution layers when their dilation rates are more than one. The causal padding is used to maintain the time consistency and input length. Additionally, max-pooling is used to compress features of the non-filtered elements in a skipped interval with the length of a dilation rate (the same color elements in Figure 2). To this end, the kernel size of the pooling layer is set as the dilation rate of the following convolution layer. Figure 2(a) depicts the base unit of LFP-TCN. The LFP module first applies the causal padding and then max-pools every non-filtered element in the skipped interval. By doing this, all elements in the interval are max-pooled first, and the compressed feature information is convoluted, propagating local feature information into higher layers. Figure 4 illustrates a toy example of the LFP module.