## 2 Materials and Methods
### Methods
#### 2.2.3 Artificial Neural Network (ANN)  
An ANN is a computational method based on the behavior of the human brain, mainly the nervous system and its connections. It therefore creates artificial models or patterns which deal with problems difficult to solve using conventional algorithm techniques. ANNs are considered nonlinear statistical data tools that can learn, memorize, and disclose the different relations in data. They model complex relationships between input and output data of an area regardless of the physical features involved. They consist of a group of units called neurons that are connected each other through several links to transmit signals. The multilayer perceptron [79] is one of the simplest and most commonly used architectures in ANNs in data analysis [80], and it was used in the current study. This model consists of several computational layers interconnected to each other where each artificial neuron (or perceptron) is directly connected to each one of the adjacent layer (Figure 4). The input data are introduced into the network through the neurons of the input layer. The hidden layers comprise neurons whose inputs come from previous layers and whose outputs go to subsequent layers. Finally, the output layer provides the outputs for the given inputs. All neurons have a bias weight. Except for the input nodes, where the information is only processed, each neural network uses as an activation function a sigmoidal function in hidden layers and a softmax function or lineal function in the output layers. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Zone 1** & **Zone 2** & **Zone 3** & **Zone 4** \\ \hline \multirow{4}{*}{k = 5} & 3080 & 4184 & 2107 & 8265 \\  & 35,215 & 26,598 & 23,286 & 42,568 \\  & 95,782 & 152,483 & 57,714 & 241,028 \\  & 259,312 & 710,000 & 107,774 & 1,600,947 \\  & 455,400 & 992,100 & 152,000 & 4,181,500 \\ \hline \multirow{4}{*}{k = 4} & 3655 & 4913 & 2352 & 17,169 \\  & 29,588 & 37,144 & 27,893 & 37,852 \\  & 187,625 & 711,000 & 75,382 & 160,947 \\  & 455,400 & 99,200 & 131,032 & 4,181,500 \\ \hline \multirow{2}{*}{k = 3} & 3655 & 4913 & 2397 & 10,258 \\  & 31,026 & 43,526 & 30,280 & 27,169 \\  & 211,968 & 851,050 & 105,618 & 2,100,473 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Final burned-area centroids using k-means algorithm (m\({}^{2}\)). The mathematical expression of a neuron is given as Equation (1):  
\[y_{i}=f(\sum_{i=1}^{N}x_{i}\omega_{i}-b_{j}), \tag{1}\]  
where \(y\) is the output of a neuron \(j,f\) is an activation function, \(xi\) is an input of the vector of inputs (\(i=1\), \(2\),..., N), \(\omega i\) is the weight associated with the connection link through which the input \(xi\) arrives to current neuron \(j\) from a neuron in the preceding layer, and \(by\) is a bias associated with neuron \(j\). The training process consists of varying weights and biases on the basis of the given inputs and aims based on the performance measure. This study used an ANN for two purposes and subsequential phases. The first phase was to classify the size of the wildfires, distinguishing between big fires (more than 30,000 m\({}^{2}\)) and small fires, which do not exceed 30,000 m\({}^{2}\) of burned area in a single wildfire. In the second phase, once wildfires were classified according to the burned area, an ANN was used to predict the burned surface for only big fires, since they account for more than 80% of the burned area in the region. Both phases consisted of three stages required for ANNs: training, validation, and testing. The aim of network training is for the ANN to be capable of reproducing the behavior of input data predicting relationships not found before by minimizing an error function. Different types of learning algorithms are used for the training stage. In this study, a backpropagation algorithm was used to train. The output errors between the output and actual target (observed data) are repeatedly propagated backwards through the network to modify weights and bias parameters.