## 2 Materials and Methods
### Determination of Land Use
#### 2.3.4 Land Use Classification Algorithms  
The information obtained from the variables was processed using the Multi-Layer Perception (MLP) modeler. MLP method is a supervised learning algorithm that is developed through training using a known data set. MLP allowed modeling and relating variables to generate a logistic regression and a powerful neural network for the development of sub-models of the studied coverages [36]. The product in raster format for the years 2000, 2010, and 2020 and the data source developed according to the variables used in the research were processed in TerrSet v.19.0.8 software. The software was downloaded on 20 January 2023 through the following website [[https://clarklabs.org/download/terrest-2020-service-update/](https://clarklabs.org/download/terrest-2020-service-update/)]([https://clarklabs.org/download/terrest-2020-service-update/](https://clarklabs.org/download/terrest-2020-service-update/)) [37] to develop the processes of the MLP method. TerrSet is an integrated geospatial system that allows for monitoring and modeling the earth system for sustainable development [38]. The pixel samples of the different equal-sized coverages that changed over time and the pixels that persisted between the two dates were used as training data in the dynamic learning process of the MLP [36]. Seventy percent of the values were used during the training stage and 30% in the validation stage. Figures 4 and 5 detail the transmission processes executed to obtain the values of the different layers of the MLP modeler. The layers are associated with a weighting weight that regulates the strength of interconnection between the variables. The neural units of the hidden layers receive as input signal the sum of the signals of the values introduced in the system and the output layers receive the sum of the signals of the values of the hidden layers [39]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Index** & **Formula** & **Characteristics** \\ \hline \hline NDVI: Normalized difference vegetation index & \(\text{NDVI}=\frac{(\text{NIR}-\text{RED})}{(\text{NIR}+\text{RED})}\) & The normalized difference vegetation index (NDVI) was used to separate the vegetation from the brightness produced by the soil and to relate photosynthetic activity and leaf structure of the plants, allowing to determine the vigorousness of the plants [33]. \\ \hline VARI: Visible vegetation index & \(\text{VARI}=\frac{(\text{GREEN}-\text{RED})}{(\text{GREEN}+\text{RED}- \text{BLUE})}\) & The visible vegetation index (VARI) allowed to observe vegetation in the visible section of the spectrum, mitigating both illumination divergences and atmospheric factors [9]. \\ \hline BSI: Bare soil index & \(\text{BSI}=\frac{[(\text{SWIR}+\text{RED})-(\text{NIR}+\text{BLUE})]}{[( \text{SWIR}+\text{RED})+(\text{NIR}+\text{BLUE})]}\) & It helps to identify areas of soil without vegetation, soils with vegetation and soils with vegetation [34]. \\ \hline NDMI: Normalized difference moisture index & \(NDMI=\frac{(NIR-\text{SWRI})}{(NIR+\text{SWRI})}\) & The Normalized Difference Moisture Index (NDMI) contributed to the detection of moisture levels in vegetation using a combination of NIR and SWIR spectral bands. It is an indicator of water stress in crops [35]. \\ \hline \hline \end{tabular} Where: _NIR_: near infrared (landsat 7: band 4; landsat 8: band 5); _RED_: (landsat 7: band 3; landsat 8: band 4); _BLUE_: (landsat 7: band 1; landsat 8: band 2); _SWRI_: band 7; _GREEN_: (landsat 7: band 2; landsat 8: band 3). \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Spectral values were obtained from Landsat 7 and Landsat 8 bands. The architecture of the model is based on a forward feed network which is composed of three layers. The first layer or input layer is composed of the variables NDVI, DEM, VARI, BSI, NDMI, and SOC. The third or output layer is made up of five units representing the categories studied and the second or hidden layer houses the model activation processes.