# Human Skeleton Data Augmentation for Person Identification over Deep Neural Network
## 5 Data Augmentation for Person Identification
### Deep Neural Network for Person Identification  
Figure 10 illustrates the architecture of the DNN. The DNN accepts the input of the anthropometric feature vectors. The dense layer, which has 512 fully connected dense nodes, is added after the input layer. The output of the dense layer can be represented by (12) as follows:  
\[\mathbf{O}_{1}=\mathbf{V}\cdot\mathbf{W} \tag{12}\]  
where \(\mathbf{W}\) is a \(25\times 512\) dimensional weight matrix. Let \(B\) be the batch selected at each epoch and \(S\) be the size of \(B\). The dimension of \(\mathbf{O}_{1}\) then becomes \(S\times 512\). Figure 10: Architecture of deep neural network for person identification. Figure 9: Anthropometric feature vectors (255 samples). To prevent overfitting and improve the speed, performance, and stability, we added a batch normalization layer after the dense layer. Hence, at the batch normalization layer, the mean of \(B\) can be calculated by (13) as follows:  
\[\mathbf{\mu}_{B}=\frac{1}{S}\sum_{s=1}^{S}\mathbf{O}_{1}(s), \tag{13}\]  
where \(\mathbf{O}_{1}(s)\) is the \(s\)th row vector of \(\mathbf{O}_{1}\) and the dimension of \(\mathbf{\mu}_{B}\) is \(1\times 512\). In addition, using \(\mathbf{\mu}_{B}\) in (13), the variance of \(B\) is  
\[\sigma_{B}^{2}=\frac{1}{S}\sum_{s=1}^{S}\left\{\mathbf{O}_{1}(s)-\mathbf{\mu}_{B} \right\}^{2} \tag{14}\]  
where \(\sigma_{B}^{2}\) has the dimension of \(1\times 512\). Let \(\mathbf{O}_{1}(s,v)\) be the \(v\)th element of \(\mathbf{O}_{1}(s)\), \(\mathbf{\mu}_{B}(v)\) be the \(v\)th element of \(\mathbf{\mu}_{B}\), and \(\sigma_{B}^{2}(v)\) be the \(v\)th element of \(\sigma_{B}^{2}\). Then, the normalized \(\mathbf{O}_{1}(s,v)\) becomes  
\[\widetilde{\mathbf{O}}_{1}(s,v)=\frac{\mathbf{O}_{1}(s,v)-\mathbf{\mu}_{B}(v)}{ \sqrt{\sigma_{B}^{2}(v)+\epsilon}} \tag{15}\]  
where \(s\in\{1,2,\cdots,S-1,S\}\), \(v\in\{1,2,\cdots,511,512\}\) and \(\epsilon\) is a small constant value added for numerical stability. In this study, the value of \(\epsilon\) is set to 0.001. Using \(\widetilde{\mathbf{O}}_{1}(s,v)\) in (15), the output of the batch normalization layer is  
\[\mathbf{O}_{2}(s,v)=\gamma(v)\cdot\widetilde{\mathbf{O}}_{1}(s,v)+\beta(v), \tag{16}\]  
where the parameters \(\gamma(v)\) and \(\beta(v)\) are learned during the optimization process of the training phase. In the DNN, the activation layer is added after the batch normalization layer. At the activation layer, we used the rectified linear unit (ReLU) activation function proposed in [46] to add non-linearity to the DNN. Therefore, the output of the activation layer is  
\[\mathbf{O}_{3}(s,v)=\max(\mathbf{O}_{2}(s,v),\ 0), \tag{17}\]  
where \(\max(a,0)\) is the function that returns \"\(a\)\" for \(a>0\) and 0 otherwise. After the activation layer, a dropout layer is added. During the training phase, at the dropout layer, input units are randomly dropped out at specified rates. In the DNN, the dropout rate is set to 0.1. The second dense layer, batch normalization layer, activation layer, and dropout layer are then successively added as described above. In addition, the number of dense nodes of the second dense layer is the same as that of the first dense layer as shown in Figure 10. At the second activation layer, the ReLU activation function is used. The dropout rate of 0.1 is set in the second dropout layer. At the end of the DNN, the softmax layer is added to classify the labels for each person. In this layer, the softmax function is used as the activation function. Therefore, the activation values from the softmax layer are normalized by:  
\[\widetilde{y}_{\theta}=\frac{\exp(y_{\theta})}{\sum_{\theta=1}^{\Theta}\exp(y _{\theta})},\ \ \forall\theta\in\{1,2,\cdots,\Theta-1,\Theta\} \tag{18}\]  
where \(\exp(\cdot)\) is the exponential function and \(\theta\) is the label for the \(\theta\)th person. In addition, \(\widetilde{y}_{\theta}\) and \(y_{\theta}\) are the normalized and unnormalized activation values, respectively.