## 2 Materials and Methods
### Methods
#### 2.2.3 Model Architecture  
The proposed MCNN-BLSTM model structure is shown in Figure 1. In this model, an ECG recording is segmented into \(n\) ECG segments and input into \(n\) branches. Each branch is a 1-dimensional CNN network, which extracts an ECG partial segment feature with a duration of \(l\) s. To improve the detection rate of AF, we combine the features extracted by every branch and use them as the input to BLSTM to enhance the temporal features. Finally, the classification is performed using a _softmax_ layer. 1. MCNN: For the MCNN considered in this study, the number \(n\) of branches is set based on the slice length \(l\) which is chosen as 6 s, 10 s, 15 s, 20 s, 25 s, and 30 s. Thus, \(n=\lceil(L_{\max})/l\rceil\), where \(L\) is the length of a short ECG recording, and \(l\) is the length of each ECG segment. Each short ECG recording has a different length. To make full use of the information from one ECG recording, we adopted the overlapping cutting scheme. The overlapping part is calculated using Equation (1). Thus, the MCNN could extract the entire short ECG recording feature, which improves the inadequacy of the 1-branch CNN (1 BCNN) that could not extract all the ECG information. In MCNN, each branch consists of 12 convolutional layers and four pooling layers, grouped by convolutional layers and separated by a pooling layer. Therefore, each 1 BCNN consists of four groups of convolutional layers. The number of convolutional layers in the four convolution groups is 4, 3, 3, and 2. The number of filters in the first group is 8, 16, 32, and 32. There are 64 filters in the second group. The third group has 128 filters. The last group of convolutional layers has 256 filters. Output data are processed using batch normalization (BN) [29] to solve the problem of an internal  
Figure 1: The architecture of the proposed model MCNN-BLSTM. covariate shift. It has the advantage of allowing the model to use a higher learning rate during the training process, which could reduce the possibility of the over-fitting of the layer. In addition, the pooling layer of each group uses average pooling (AP), and the last layer uses global average pooling (GAP). The pooling layer has the advantages of data dimensionality reduction, nonlinear transformation, and expansion of the perception field. In each branch, the pooling layer step size is set to four to quickly reduce the computational complexity and capture the local features between the ECG recordings within a short time window. The last group of convolutions is used by the GAP instead of the AP. GAP [30] mainly performs a pooling of the entire feature map of the last layer to form a feature point. It is mainly proposed to solve the problem of full connection, as there are too many parameters in the full connection operation. One advantage of GAP over a fully connected layer is that it has no parameters that need to be optimized. Thus, overfitting of the layer is avoided. Additionally, GAP can extract spatial information and is more robust to the spatial transformation of the inputs. Let \(f_{k}(a,b)\) be the activation value of element \(k\) in the last convolutional layer on the feature space location \((a,b)\). For unit \(k\), the result \(F_{k}=\sum_{a,b}f_{k}(a,b)\) of the GAP was obtained. 2. LSTM: LSTM is one kind of recurrent neural network. Unlike the traditional RNN, LSTM can effectively deal with the long-term dependence of temporal signals [31].