# A Machine Learning Approach for Mapping Chlorophyll Fluorescence at Inland Wetlands
## 2 Materials and Methods
### Model Establishment and Evaluation  
The XGBoost algorithm was investigated to build a model for estimation of chlorophyll fluorescence, which is an open-source software library for gradient boosting algorithms that is designed to be highly efficient, flexible, and scalable. It is a popular machine learning framework that is widely used in industry and academia for supervised learning tasks, such as classification and regression. The XGBoost algorithm works by combining multiple weak models to create a strong model. It trains each model iteratively by adjusting the weights of misclassified samples, with the aim of minimizing a loss function. The final model is a weighted sum of all the models, with the weights determined by their performance on the training data [76]. XGBoost is known for its speed and performance, and it supports regularization, uses the power of parallel processing, handles missing values, and performs cross-validation [77].  
The input for the model was an array containing r rows and c columns, where r represents the total number of observations with available data on predictors (vegetation indices) and references (Fv/Fm), and c represents the number of columns with predictors calculated for each growth stage. All the predictors were scaled to a range of values between zero and one. The proposed model in supervised learning referred to the mathematical structure by which the prediction was made from the satellite-based vegetation indices (listed in Table 2). A linear prediction model was created, which calculates predictions based on a combination of weighted satellite-derived data and parameters. The available dataset was split into a training set and a validation set in a ratio of 80:20. To improve the accuracy of the prediction model, the XGBoost algorithm was fine-tuned using tenfold cross-validation and learning curve methods during the training phase to determine the best parameter configuration.  
In order to evaluate the performance of the model, a cross-validation was carried out using the leave-one-out approach, which is a variant of k-fold cross-validation, where k is equal to the number of observations in the dataset. It should be noted that the feature selection process was repeated at each iteration to prevent the model from benefiting from knowledge of the data used for validation. The model performance was assessed using various metrics, including the coefficient of determination (R\({}^{2}\)), which is the square of the correlation coefficient, as well as the mean absolute error (MBE), root mean square error (RMSE), and relative root mean square error (RRMSE).  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Application** & **Abbreviation** & **Name** & **Equation** & **Citation** \\ \hline \multirow{7}{*}{\begin{tabular}{} \end{tabular} } & SIPI & \begin{tabular}{c} Structure Insensitive \\ Pigment Index \\ \end{tabular} & \begin{tabular}{c} SIPI = \(\frac{R_{402}-R_{410}}{R_{842}+R_{465}}\) \\ \end{tabular} & [69] \\ \hline \multirow{7}{*}{\begin{tabular}{} \end{tabular} } & GVMI & \begin{tabular}{c} Global Vegetation \\ Moisture Index \\ \end{tabular} & GVMI = \(\frac{(R_{402}+0.1)-(R_{250}+0.2)}{(R_{402}+0.1)+(R_{250}+0.2)}\) \\ \cline{2-4}  & MSI & Moisture Stress Index & MSI = \(\frac{R_{150}}{R_{82}}\) & [71] \\ \cline{2-4}  & NDII & \begin{tabular}{c} Normalized Difference \\ Infrared Index \\ \end{tabular} & NDII = \(\frac{R_{402}-R_{410}}{R_{842}+R_{410}}\) & [72] \\ \cline{2-4}  & NDWI & \begin{tabular}{c} Normalized Difference \\ Water Index \\ \end{tabular} & NDWI2 = \(\frac{R_{402}-R_{2100}}{R_{842}+R_{2100}}\) & [73] \\ \cline{2-4}  & NMDI & \
\begin{tabular}{c} Normalized Multi-band \\ Drought Index \\ \end{tabular} & NMDI = \(\frac{R_{405}-(R_{4100}-R_{2100})}{R_{408}+(R_{1840}-R_{2200})}\) & [74] \\ \cline{2-4}  & SIWSI &
\begin{tabular}{c} Shortwave Infrared Water \\ Stress Index \\ \end{tabular} & SIWSI = \(\frac{R_{405}-R_{410}}{R_{845}+R_{4100}}\) & [75] \\ \hline \end{tabular}
\end{table}
Table 2: _Cont._