## 4 Results
### Gradient Boosting Analysis Using XGBoost  
After samples have been collected, the XGBoost models are built using a grid search among the parameter space. XGBoost (eXtreme Gradient Boosting) is a fast implementation of gradient boosting [36]. It is a scalable end-to-end tree boosting system that has been widely used and achieves state-of-the-art classification and regression performance [37]. It can improve in the reduction of overfitting, the parallelization of tree construction, and the acceleration of execution. It is an ensemble of regression trees known as CART [38]. The prediction score is calculated by adding all of the trees together, as indicated in the following equation,  
\[\hat{Y}=\sum_{m=1}^{M}f_{m}(X) \tag{1}\]  
where \(M\) is the number of trees and \(f_{m}\) is the mindependent CART tree. In contrast to [PERSON]'s [39] original gradient boosting architecture, XGBoost adds a regularized objective to the loss function. The regularized objective for the \(m\)th iteration optimization is provided by  
\[L^{m}=\sum_{i=1}^{n}l(y_{i},\hat{y_{i}}^{m})+\sum_{j=1}^{m}\Omega(f_{j}) \tag{2}\]  
where \(n\) denotes the number of samples, \(l\) denotes the differentiable loss function that quantifies the difference between the predicted \(\hat{y_{i}}^{m}\) and the target \(y_{i}\) and \(\Omega\) denotes the regularization term  
\[\Omega(f)=\gamma T+\frac{1}{2}\lambda\sum_{k=1}^{T}{w_{k}}^{2} \tag{3}\]  
where \(T\) is the number of nodes and \(w\) denotes each node's weight. The regularization degree is controlled by two constants, \(\gamma\) and \(\lambda\). Furthermore, taking into account that for the \(m\)th iteration the following relation holds,  
\[\hat{y_{i}}^{m}=\hat{y_{i}}^{m-1}+f_{m}(x_{i}) \tag{4}\]  
we can recast Equation (2) as,  
\[L^{m}=\sum_{i=1}^{n}\left[l\left(y_{i},\ y_{i}^{m-1}\right)+g_{i}f_{m}(x_{i}) +\frac{1}{2}h_{i}{f_{m}}^{2}(x_{i})\right]+\Omega(f_{m}) \tag{5}\]  
where we introduced the operators, \(g_{i}=\partial_{g^{m-1}}l\left(y_{i},\hat{g}^{m-1}\right)\) and \(h_{i}=\partial^{2}_{g^{m-1}}l\left(y_{i},\ \hat{g}^{m-1}\right)\), which are the loss function's first and second-order derivatives, respectively. XGBoost makes the gradient converge quicker and more accurately than existing gradient boosting frameworks by using the second-order Taylor expansion for the loss function [36]. It also unifies the generation of the loss function's derivative. Furthermore, adding the regularization term XGBoost to the target function balances the target function's decrease, reduces the model's complexity, and successfully resolves overfitting [36]. Furthermore, XGBoost can use the weight to determine the importance of a feature. The number of times a feature is utilized to partition the data across all trees is the weight in XGBoost [36], and is given by the equation \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline
**Spearman correlation coefficient (r)** & 0.06835 \\ \(p\)**-value** & 0.0000375 \\
**Covariance** & 161,169,282.6 \\
**Sample size (n)** & 3632 \\
**Statistic** & 4.1275 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Spearman correlation between _swti_rank and _alexa_rank. \[IMP^{F}=\sum_{m=1}^{M}\sum_{l=1}^{L-1}I\left(F^{l}{}_{m},\ F\right)I\left(F^{l}{}_{m},\ F\right) \tag{6}\]  
with the boundary conditions, \(IMP^{F}=1\), if \(F^{l}{}_{m}==F\), else \(IMP^{F}=0\). \(M\) is the number of trees or iterations, \(L\) denotes the number of nodes in the \(m\)th tree, \(L-1\) denotes the tree's non-leaf nodes, \(F^{l}{}_{m}\) stands for the corresponding feature to node \(l\), and \(I()\) denotes the indicator function. The Alexa ranking for the websites under investigation is used as the outcome of the fitted model. The features collected by the crawling mechanism are used as the predictor variables. Since the main point of the analysis is to identify the most important features related to semantic web technologies with respect to the ranking of a website, we perform a grid search for the parameter space of XGBoost.