# Soybean Cultivars Identification Using Remotely Sensed Image and Machine Learning Models
## 2 Materials and Methods
### Using Machine Learning Models  
The models tested were: artificial neural networks (ANN), radial basis function (RBF) network, the decision tree algorithms J48 (DT) and reduced error pruning (REPTree), random forest (RF), and support vector machine (SVM). The ANN tested consists of a single hidden layer formed by a number of neurons that is equal to the number of attributes, plus the number of classes, all divided by 2. The J48 algorithm (DT) is a classifier for generating a C4.5 decision tree with an additional pruning step based on reduced-error strategy [17; 18]. RBF is a feed-forwarded network in which training is performed in a hidden layer, implementing a normalized Gaussian radial basis function and the k-means clustering algorithm for the basis function of this hidden layer, and supervised learning is used for the output layer [19]. REPTree uses the decision tree logic and creates several \begin{table}
\begin{tabular}{l c} \hline \hline
**Vegetation Indices** & **Equations** \\ \hline AFRI1600 (Aerosol Free Vegetation Index 1600) & \(\left(R\lambda_{nir}-0.66*R\lambda_{nir}\right)/(R\lambda_{nir}+0.68\lambda_{ nir})\) \\ ARVI2 (Atmospherically Resistant Vegetation Index 2) & \(-0.18+1.17*((R\lambda_{nir}-R\lambda_{nir}-R\lambda_{nir}+R\lambda_{nrel}))\) \\ ATSAVI (Ajusted Transformed Soil-Ajusted VI) & \(1.22*\left[\frac{(R\lambda_{nir}-1.22*R\lambda_{nir}-0.03)}{(112*R\lambda_{nir} +R\lambda_{nrel}-1.22*0.03+0.08(1+1.22))}\right]\) \\ EVI (Enhanced Vegetation Index) & \(2.5*\left(\frac{R\lambda_{nir}-R\lambda_{nrel}}{(R\lambda_{nir}+R\lambda_{nrel}- 7.5*R\lambda_{nir})+1}\right)\) \\ EVI2 (Enhanced Vegetation Index 2) & \(2.5*(R\lambda_{nir}-R\lambda_{nrel})/(R\lambda_{nir}+2.4*R\lambda_{nrel}+1)\) \\ GNDVI (Green Normalized Difference Vegetation Index) & \(\frac{(R\lambda_{nir}-R\lambda_{nir})}{(R\lambda_{nir}+R\lambda_{nir})}\) \\ GRNDVI (Green-Red NDVI) & \([R\lambda_{nir}-\left(R\lambda_{green}+R\lambda_{nrel}\right)]/[R\lambda_{nir} +\left(R\lambda_{green}+R\lambda_{nrel}\right)\) \\ GVI (Tasselled Capvegetation) & \(-0.284*R\lambda_{nir}-0.2435*R\lambda_{green}-0.5436*R\lambda_{nrel}+0.7243* \\ R\lambda_{nir}+0.0840*R\lambda_{nir}\) & \(R\lambda_{nir}-0.1800*R\lambda_{SWIR2}\) \\ GVMI (Global Vegetation Moisture Index) & \(\frac{(R\lambda_{nir}+0.1)-(R\lambda_{nir}+0.02)}{(R\lambda_{nir}+0.01)-(R \lambda_{nir}+0.02)}\) \\ MNDVI (Modified Normalized Difference Vegetation Index) & \(\frac{(R\lambda_{nir}-R\lambda_{nir})}{(R\lambda_{nir}+R\lambda_{nir})}\) \\ NDVI (Normalized Difference Vegetation Index) & \(\frac{(R\lambda_{nir}-R\lambda_{nir})}{(R\lambda_{nir}+R\lambda_{nir})}\) \\ SBI (Tasselled Cap—brightness) & \(0.3037*R\lambda_{nir}+0.2793*R\lambda_{green}+0.4743*R\lambda_{nrel}+0.5585*\) \\ \(R\lambda_{nir}+0.5082*R\lambda_{Cirrus}+0.1863*R\lambda_{SWIR2}\) \\ SIWSI (Normalized Difference 860/1640) & \(\frac{(R\lambda_{nir}-R\lambda_{SWIR2})}{(R\lambda_{nir}+R\lambda_{SWIR})}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vegetation spectral models calculated from spectral bands obtained via Landsat 8 Collection 1 Tier 1 and real-time data TOA reflectance. trees in different iterations. Afterwards, it selects the best tree using the information gain and performs the reduced-error pruning as splitting criterion [20]. The RF model is able to produce multiple decision trees for the same dataset and uses a voting scheme among all these learned trees to classify new instances [21]. SVM performs classification tasks by building hyperplanes in multidimensional space to distinguish different classes [22]. The classification of the five soybean cultivars was performed by the six ML models in a 10-fold stratified randomized cross-validation with ten repetitions (100 runs for each model). Different inputs were considered for each classification model: spectral bands only (SBs), vegetation indices only (VIs), and SBs + VIs. The parameters obtained for performance evaluation of the models and inputs were correct classification (CC, %) and Kappa coefficient.