## 3 The Proposed Model
### Training and Detection Using ConvLSTM  
The training and detection phases are necessary to create a model in the training phase that can be used in the detection phase to identify anomalies in the WBAN, utilizing a deep learning approach. This technique has been widely implemented in healthcare applications because of its capacity to automatically detect complicated features without requiring domain expertise. The model developed in this paper is based on the hybrid ConvLSTM technique, which is a hybridization of the long short-term memory model and convolutional deep neural networks. (a) Convolutional LSTM (ConvLSTM)  
The hybrid deep learning system developed in this study combines the principles of convolutional and LSTM models. ConvLSTM is a type of RNN that is capable of capturing spatial-temporal data [24]. The convolutional component acquires the spatial area data, while the LSTM component leverages the temporal area data. However, the data, which are in the form of time series from the different sensors, have both spatial and temporal links. Thus, ConvLSTM can be employed as an important framework for anomaly detection problems involving time series data [25]. The ConvLSTM captures and applies both temporal and spatial correlations to predict the future state of a network cell, based on the inputs and previous states of its nearest neighbors. This is accomplished by including a convolution operation into the matrix multiplication step that is used in traditional fully integrated LSTM state-to-state and input-to-state transitions [24]. The ConvLSTM consists of multiple gates; the data flow may be stated using Equations (2)-(7). \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Time and Date** & **HR** & **ABPSys** & **ABPDias** & **ABPMean** & **PULSE** & **RESP** & **SpO\({}_{2}\)** \\ \hline
14:07:00 10/11/15 & 77.6 & 157.4 & 66.1 & 100.5 & 77.9 & 23 & 97.4 \\ \hline
14:08:00 10/11/15 & 77.3 & 149.2 & 62.6 & 95 & 77.6 & 22.2 & 97 \\ \hline
14:09:00 10/11/15 & 76.1 & 150.5 & 62.4 & 95.1 & 76.8 & 22.3 & 97 \\ \hline
14:10:00 10/11/15 & 73 & 158.4 & 65.4 & 99.8 & 74.3 & 22.2 & 97.4 \\ \hline
14:11:00 10/11/15 & 75.6 & 152.4 & 63.3 & 96.7 & 76.4 & 22.4 & 97.5 \\ \hline
14:12:00 10/11/15 & 75 & 154.3 & 63.4 & 97.1 & 75.4 & 22.2 & 97.5 \\ \hline
14:13:00 10/11/15 & 75.2 & 150.3 & 62.1 & 94.7 & 76.7 & 22.1 & 97.6 \\ \hline \end{tabular}
\end{table} 
Table 2: The dataset’s sample sensor readings. The weighted sum of each gate's inputs is given a sigmoid function, which is then used as the activation function [26]:  
\[\mathrm{f_{t}}=\sigma\Big{(}W_{\mathrm{xf}}\bigotimes X_{t}+W_{\mathrm{hf}} \bigotimes H_{t-1}+W_{\mathrm{cf}}\bigodot C_{t-1}+B_{f}\Big{)} \tag{2}\]  
where \(f_{t}\) is the forget gate's output, which regulates the data that are lost in the previous cell state. \(C_{t-1}\), \(W_{\mathrm{xi}}\) is the convolution kernel used for the input tensor \(X_{t}\) in the input gate, \(X_{t}\) is the input tensor at time \(t\), \(W_{\mathrm{hf}}\) is the convolution kernel used for the input tensor \(H_{t-1}\) in the forget gate, \(H_{t-1}\) is the output tensor from the cell at time \(t-1\), \(W_{\mathrm{cf}}\) is the weight that is used for the old cell state \(C_{t-1}\) in the forget gate, \(C_{t-1}\) is the cell state at time \(t-1\), and \(B_{f}\) is the bias in the forget gate. \[\dot{\mathrm{\epsilon_{t}}}=\sigma\Big{(}W_{\mathrm{xi}}\bigotimes X_{t}+W_{ \mathrm{hi}}\bigotimes H_{t-1}+W_{\mathrm{ci}}\bigodot C_{t-1}+B_{i}\Big{)} \tag{3}\]  
Here, \(\dot{\mathrm{\epsilon_{t}}}\) is the output of the input gate, \(W_{\mathrm{xi}}\) is the convolution kernel used for the input tensor \(X_{t}\) in the input gate, \(W_{\mathrm{hi}}\) is the convolution kernel used for the input tensor \(H_{t-1}\) in the input gate, \(W_{\mathrm{ci}}\) is the weight that is used for the old cell state \(C_{t-1}\) in the input gate, and \(B_{i}\) is the bias in the input gate.