## 3 Data and Methods
### Flash-Flood Potential Assessment
#### 3.3.3 Description and Configuration of Multilayer Perceptron (MLP) Model for FFPI Computation  
In order to avoid the noisy data within the machine learning models and also in order to reduce the redundant information used in the training process, the predictive ability of the flash-flood predictors will be assessed. The predictive ability was estimated through the linear support vector machine, implemented in Weka 3.9 software developed by the Univerisity of Wakaito, Hamilton, New Zealand. The multilayer perceptron (MLP) is a type of neural network that contains many interconnected nodes whose main aim is to solve the complex problems regarding the spatial relationships between influencing variables and the presence of a phenomenon. In the present case study, the influencing variables were flash-flood predictors, while the flash-flood location represented the dependent variable. A detailed description of the MLP background was carried out by [PERSON] and [PERSON] [86] and  
Figure 5: The factors considered for the FFPI calculation: (**a**) convergence index, (**b**) aspect, (**c**) modified Fournier index (1989), and (**d**) modified Fournier index (2019). [PERSON] et al. [93]. The MLP architecture is composed of three main elements: (i) the input layer that contains the input neurons represented by flash-flood conditioning factors; (ii) the hidden layer, which has a various number of hidden neurons that have a crucial role in the MLP training procedure; and (iii) the output layer, which in the present case study, contained two neurons represented by flash-flood locations and non-flash-flood locations. An extremely important role in the MLP algorithm is held by the number of hidden neurons within the hidden layer. In this case, the number of hidden neurons was established based on the following formula [85,104]: \(2\times\text{N}+1\), where N is the number of flash-flood predictors. Thus, 21 hidden neurons were included in the hidden layer (Figure 6). The training sample of flood and non-flood locations for 1965-1989 and 1990-2019, together with the 10 flash-flood predictors, was used in order to train the MLP model. It should be mentioned that in the case of flash-flood predictors used in the MLP, the classes/categories were assigned the frequency ratio values calculated using Equation (3) [105]:  
\[FR=\left(\frac{N(FXi)}{\sum_{i=1}^{m}N(FXi)}\right)\!\!\left/\left(\frac{N(Xj) }{\sum_{j=1}^{n}N(Xj)}\right)\right. \tag{3}\]  
where \(FR\) is the value of frequency ratio assigned to a class/category \(i\) of parameter \(j\), \(N(FXi)\) is the number of flash-flood locations in a class \(i\) of a variable \(X\), \(N(Xj)\) is the number of pixels inside a variable \(Xj\), \(m\) is the number of classes contained by a flash-flood predictor \(Xi\), and \(n\) is the number of flood-influencing factors inside the research zone. Figure 6: MLP architecture. Furthermore, the \(FR\) coefficients, obtained for the two periods, were normalized between 0.1 and 0.9 using the Equation (4):  
\[v=\frac{(a-\min(r))\times(\max(l)-\min(l))}{\max(r)-min(r)}+min(l) \tag{4}\]  
where \(v\) represents the standardized value of \(a\), \(a\) represents the current value of the variable, \(r\) represents the limits of the range value, and \(l\) represents the limits of the standardization range. The normalized values of \(FR\) were used as input data in MLP algorithm for determining FFPI\({}_{1989}\) and FFPI\({}_{2019}\). Thus, the MLP model was trained by using a maximum of 500 epochs and 30 validation thresholds. The values of the root mean square error (RMSE) for both years were also determined in order to assess the model efficiency. By applying the MLP algorithm using Weka 3.9 software, the importance of each flash-flood predictor was calculated. By multiplying the values of the MLP importance with the \(FR\) coefficients in ArcGIS 10.5, the FFPI\({}_{1989}\) and FFPI\({}_{2019}\) were derived.