# An Advanced Soil Classification Method Employing the Random Forest Technique in Machine Learning
## 4 Soil Classification Using Random Forest Method
### Model Construction  
The process of initializing the RF model begins with a predetermined number of decision trees. Subsequently, it undergoes training on the designated dataset, where each tree's growth occurs through the utilization of a bootstrap sample of the data. At each node, the model selects the optimal split based on a subset of features. Illustrated in Figure 5, the RF's architecture involves the assembly of multiple decision trees, with each tree constructed independently utilizing a random subset of the training data and input features. For this study, the training and testing datasets constitute 70% and 30% of the total data, respectively. Throughout the training phase, each tree expands either until it reaches its maximum depth or meets a specified stopping criterion, such as the minimum number of samples required for node splitting or a maximum depth threshold. Once all the decision trees are built, predictions are produced by consolidating the outputs from each individual tree. In regression tasks, the final prediction is typically the average of all tree predictions, while in classification tasks, it is usually determined by a majority vote among the trees. The inclusion of randomness in the construction of each tree aids in diminishing correlations among the trees and mitigating the risk of overfitting. Assuming there exists a database \(D\), it can be represented as follows:  
\[\big{(}x_{i},y_{i}\big{)}\text{ for }i=1,\ 2,\ldots,\ N\ \&\ x_{i1},x_{i2}, \ldots,x_{ip}, \tag{4}\]  
In this equation, \(x\), \(y\), \(N\), and \(p\) are the input, output, data number, and number of factors. If \(D\) is divided into \(M\) regions and \(D_{1},D_{2},\ldots,D_{M}\) is obtained, and a constant \(c_{m}\) is used to represent the simulated output \(f(x)\) of each region, the following equation can be obtained:  
\[f(x)=\sum_{m=1}^{M}c_{m}I(x\in D_{m}), \tag{5}\]  
Figure 4: Variable importance plot using the OOB predictor (green indicates that the OOB variable importance is negative, gray represents an OOB variable importance between 0 and 6, and red signifies an OOB variable importance greater than 6). where \(I\) is an indicator function. By incorporating the least squares sum as a criterion, the optimal constant, \(\hat{c}_{m}\), can be obtained as the average of the output values, \(D_{m}\), within the region:  
\[\hat{c}_{m}=average\left(y_{i}|x_{i}\in D_{m}\right). \tag{6}\]  
Assuming the presence of a categorical variable \(j\) and a designated split point \(s\), the database is partitioned into two distinct subsets, as indicated by the following equation:  
\[D_{1}(j,s)=\big{\{}x\big{|}x_{j}\leq s\big{\}}\text{ and }D_{2}(j,s)=\big{\{}x \big{|}x_{j}>s\big{\}}. \tag{7}\]  
As per the preceding equation, the quest for the suitable categorical variable \(j\) and split point \(s\) results in the following equation:  
\[\min_{j,s}\left[\min_{c_{1}}\sum_{x_{i}\in D_{1}(j,s)}(y_{i}-c_{1})^{2}+\min_{ c_{2}}\sum_{x_{i}\in D_{2}(j,s)}(y_{i}-c_{2})^{2}\right]. \tag{8}\]  
Referring to the equation above, the internal minimization for any combination of \(j\) and \(s\) can be deduced from the subsequent expression:  
\[\hat{c}_{1}=average\left(y_{i}|x_{i}\in D_{1}(j,s)\right)\ \ \&\ \ \hat{c}_{2}=average\left(y_{i}|x_{i}\in D_{2}(j,s)\right). \tag{9}\]  
Utilizing the aforementioned equations, the optimal pair (\(j\), \(s\)) can be determined, facilitating the partitioning of the data into two regions. Iterating through the described computations enables the data to be sequentially split into all resulting regions. If a decision tree \(T\) partitions the data into \(D_{m}\) regions via \(m\) nodes, where \(N_{m}\) represents the total number of regions, \(\hat{c}_{m}\) can be articulated as follows:  
\[\hat{c}_{m}=\frac{1}{N_{m}}\sum_{x_{i}\in D_{m}}y_{i}. \tag{10}\]  
Bagging, or bootstrap aggregation, is a technique employed to acquire an aggregated predictor by creating numerous predictor variations and amalgamating them.