## 2 Theoretical Background
### Cnn  
CNN is characterized by being an innovative deep-learning architecture suitable for pattern recognition in images. In this regard, it employs a single block for identifying and classifying the encountered patterns or features into images in order to associate them automatically with a phenomenon studied, eliminating the hand engineering during the selection and test of features/patterns [25]. For performing this task, it is constituted by four sub-CNNs known as convolutional-, pooling-, fully connected-, and softmax-layer, as displayed in Figure 4.  
According to the sequence or structure shown in Figure 3, the analyzed images, \(I_{\text{m}}\), (with dimension \(h\times\omega\)) are convolved, i.e., \(\ast\), with a set of convolutional filters, \(F_{\text{i}}\), in order to identify or extract diverse features from the evaluated images as follows [26]:  
\[X_{i}=\sigma(\sum F_{i}\ast I_{m}+B_{i}) \tag{8}\]  
where \(\sigma\) and \(B\) imply a nonlinear activation function and a bias term, respectively. To perform this task, each convolutional filter (with a dimension of \(k_{1}\times k_{2}\)) is convolved with a region or local section of the evaluated image with a stride \(s_{1}\). Hence, the output, \(X_{i}\), is deemed as the maps of patterns estimated by each convolutional filter, which present a dimension of \(z_{1}\times z_{2}\) and is determined by [27]:  
\[z_{1}=\frac{h-k_{1}+2p}{s_{1}}+1 \tag{9}\]  
Figure 4: CNN architecture.  
Figure 3: Procedure to combine the IMFs estimated by EMD-based methods into an image.  
\[z_{2}=\frac{\omega-k_{2}+2p}{s_{1}}+1 \tag{10}\]  
where \(p\) is a padding parameter, which usually receives a value of 1 with the aim of providing the same spatial resolution for the output and input [27]. The nonlinear activation function recognized as ReLu (\(f(y_{i})=\max(0,X_{i})\)), i.e., rectified linear unit, has demonstrated to be the fastest and most suitable function for learning and encountering relevant patterns of each map of patterns in a CNN [28].  
Once the feature or characteristic maps are estimated by means of the convolutional layer, they are utilized as inputs to the subsequent layer named pooling layer, which is utilized for subsampling or reducing the dimensionality of the estimated feature maps with the goal of reducing the number or quantity of patterns to be analyzed by next layer or sub-CNN [29]. Particularly, it applies or passes a filter with a size \(K_{1}\times K_{2}\) and stride \(s2\) on the feature maps for obtaining their maximum (identified as max pooling) of the neighbor values designated by the utilized filter. Thus, the decreased or reduced pattern maps, \(Y_{i}\), with sizes of \(Z_{1}\times Z_{2}\), are estimated as follows [28]:  
\[Z_{1}=\frac{z_{1}-K_{1}}{s_{2}}+1 \tag{11}\]  
\[Z_{2}=\frac{z_{2}-K_{2}}{s_{2}}+1 \tag{12}\]  
It is worth noting that max pooling has demonstrated to be efficient to enhance the generalization performance and capture invariant patterns [30]. For these reasons, it is employed in this work for identifying the most suitable patterns.  
The features estimated by the pooling layer are utilized as input of a traditional multilayer perceptron named fully connected layer, which has the aim of performing the pattern recognition/classification. Finally, a SoftMax layer is utilized for creating the required outputs, in this case, the SCD prediction, through a softmax transfer function. In [27], a more detailed description of CNN can be found.  
As there is no specific CNN structure that performs well for any application, mainly considering the computational complexity, in this work, different sizes of input images, different numbers and sizes of filters, as well as different numbers of epochs and sizes of batch are also investigated.