*2.5. Machine Learning Algorithm of Modeling FSV*

The random forest (RF) is a machine learning algorithm that uses multiple decision tree classifiers for classification and prediction. In recent years, studies on RF algorithms have rapidly developed accompanied by large numbers of applied research carried out in many fields. The RF algorithm is an efficient bagging-based integrated learning algorithm, and numerous prior studies have shown that the RF algorithm performs well in regression prediction [35–38]. Therefore, this study chooses the RF algorithm for modeling and analysis. The RF algorithm operates by utilizing the bootstrap method, that involves randomly sampling from the original population to create multiple samples. These samples are then used to generate a set of decision trees (ntree). The RF algorithm achieves higher accuracy and robustness by increasing the number of decision trees. At each splitting node, the RF algorithm randomly selects a subset of predictors (mtry) to build each tree. Additionally, there is no need to prune each tree. The RF algorithm employs the "out-ofbag" (OOB) error procedure to independently build each tree based on the training data. This procedure allows for the calculation of variable importance (VI) and OOB error for each tree grown by the RF algorithm. An estimation of the OOB error can be obtained using the following formula:

$$\text{COB}\_{\text{error}} = \frac{1}{n} \sum\_{i=1}^{n} (y\_i - \hat{y}\_i)^2 \tag{2}$$

where *yi* is the measured FSV, *y*ˆ*<sup>i</sup>* is the predicted FSV, and *n* is the total number of OOB samples.

In this study, three RF-based models composed of bands and vegetation indices (VIs) to estimate FSV, namely the bands-based model (BBM), VIs-based model (VBM), and bands + VIs-based model (BVBM) have been used.
