# A Novel Method of Emotion Recognition from Multi-Band EEG Topology Maps Based on ERENet
## 2 Materials and Methods
### An Emotion Recognition Method from Multi-Band EEG Topology Maps Using ERENet
#### 2.3.2 The Model of Proposed ERENet
In the classical CNN models, a pooling layer is usually added after the convolution layer to reduce the data dimension, which often leads to the loss of some information. In the EEG-based recognition tasks, the size of the EEG topology is much smaller than the image used in the field of computer vision. Therefore, the pooling operation is not used after the convolution layer in this study for preserving all information. After the group convolution layer, the BN layer is added to normalize the data distribution, which does not only avoid the gradient disappearance or explosion and make the gradient more predictable and stable, but also increases the training speed. Finally, the final feature representation \(U\) of the module is obtained through the activation of the Relu activation function, as shown in Equation (5):  
\[U=\left\{U_{i}^{j}\in\mathbb{R}^{h\times w}\left|U_{i}^{j}=RELU\left(BN\left(T _{i}^{j}\right)\right),i=1,2,\ldots,\mu;j=\theta,\alpha,\beta,\gamma\right\}, \tag{5}\]  
where \(U_{i}^{j}\in\mathbb{R}^{h\times w}\) represents the \(i\)-th feature representation of the band \(j\). Moreover, \(U\) is output to the next module. that each group \(U_{i}=\left\{U_{i}^{\theta},U_{i}^{\alpha},U_{i}^{\beta},U_{i}^{\gamma}\right\} \in\mathbb{R}^{h\times w\times 4}(i=1,2,\ldots,\mu)\) of feature maps contains feature maps from different frequency bands. \(U_{i}\) is set with \(\mu\) convolution kernels for convolution, respectively, with stride of 1, and the boundaries of the feature maps are filled with 0. The convolution result \(V_{i}\) of \(U_{i}\) is shown in Equation (6):  
\[V_{i}=Conv2D\_i(U_{i})=\left\{V_{i}^{1},T_{i}^{2},\ldots,T_{i}^{\lambda}\right\},\;V_{i}\in\mathbb{R}^{h\times w\times\lambda},\;i=1,2,\ldots,\mu, \tag{6}\]  
where \(V_{i}^{j}\in\mathbb{R}^{h\times w}\) represents the \(i\times j\)-th feature map. After convolution of \(\mu\) groups of feature maps, \(\mu\times\lambda\) different fusion feature maps can be obtained. After convolution operation, the BN layer is also set to normalize the data distribution, and the final feature representation \(H\) of the module is obtained through the Relu activation layer and output to the next module, as shown in Equation (7):  
\[H=\left\{H_{i}^{j}\in\mathbb{R}^{h\times w}\Big{|}H_{i}^{j}=RELU\Big{(}BN \Big{(}V_{i}^{j}\Big{)}\Big{)},i=1,2,\ldots,\mu;j=1,2,\ldots,\lambda\right\}, \tag{7}\]  
where \(H_{i}^{j}\in\mathbb{R}^{h\times w}(i=1,2,\ldots,\mu;j=1,2,\ldots,\lambda)\) represents the \(i\times j\)-th feature representation. 3. Weighted Classification Module  
The structure of the weighted classification module shown in the right box of Figure 4 includes a channel-weighted pooling layer, a fully connected layer, and an output layer with a Sigmoid activation function. In the traditional CNN, the fully connected layer also accounts for abundant parameters in addition to the convolution layer. For example, when MobileNets [49] is applied to Imagenet dataset for classification, the fully connected layer uses 1024 feature vectors as input and generates 1000 probability values, corresponding to 1000 classes. The number of parameters is more than one million, accounting for 24.33% of the total parameters. Therefore, channel-weighted pooling is proposed to replace the fully connected layer in the weighted classification module, which not only aggregates features, but also reduces abundant parameters in the classification layer. In order to filter all the fused features and further extract features, all feature maps are directly considered instead of performing the convolution operation on a feature map from the beginning to the end, the feature values at the same position of \(\mu\times\lambda\) feature maps are aggregated, and each position is given a learnable weight according to its importance.