# Hybridizing Fuzzy String Matching and Machine Learning for Improved Ontology Alignment
## 3 Preliminaries
### Decision Tree Regression  
A Decision Tree is a data structure consisting of an arbitrary number of nodes and branches at each node, which is widely used in machine learning. Decision Tree Regression (DTR) employs a rapid divide-and-conquer greedy algorithm that recursively divides the data into smaller sections. This algorithm repeatedly selects the feature that maximizes the information gain and then partitions the data based on the selected feature, eventually creating a tree structure that provides a sequence of decision rules for prediction purposes [54]. The algorithmic process of the Decision Tree involves determining the predictive accuracy criteria, which can be achieved through various methods such as test sample error, cross-validation error, or re-substitution error. After defining the accuracy criteria, the next step involves selecting the optimal split based on the chosen criteria. Finally, the algorithm determines the stopping point for splitting and selects the optimal tree structure [55]. Inthe first step, the re-substitution error is computed using the same dataset that was utilized to build the predictor \(p\). This error is calculated as the Mean Squared Error between the predicted values and the actual values of the dataset. To calculate the cross-validation error in Decision Tree regression, the dataset is partitioned into \(k\) subsets, referred to as \"folds\". The model is then trained on \(k-1\) folds, while the remaining fold is used for testing. This process is repeated \(k\) times, with each fold serving as the test set once. The resulting \(k\) testing errors are averaged to compute the cross-validation error. By evaluating the model's performance on multiple test sets, the cross-validation error provides a more reliable measure of the model's ability to generalize to new data and prevent overfitting. The sample error is calculated by dividing the total number of cases into two subsamples, \(X_{1}\) and \(X_{2}\), with sizes of \(N_{1}\) and \(N_{2}\), respectively.  
In the second step, the splits are selected, then evaluated based on the measure of node impurity. The most commonly used method for this is the Least-Squared Deviation, which is represented in Equation (9) [55].  
\[R(t)=\frac{1}{N_{w}(t)}{\sum_{i\in t}w_{i}f_{i}(u_{i}-\overline{v}(t))}^{2} \tag{9}\]  
where \(N_{w}\) is the weighted number of cases in node \(t\), \(w_{i}\) is the value of weighting variable for case \(i\),\(f_{i}\) represents the value of the frequency variable, \(u_{i}\) is the value of the response variable, and \(\overline{v}(t)\) is the weighted mean for node t.  
In the last step, the determination of when to stop splitting takes place, and this relies on the minimum number of nodes. The selection of the right-sized tree (called the optimum tree) comes next, and it is obtained by using what is called tree pruning to reduce the risk of overfitting and improve the model's generalization performance. Tree pruning involves removing branches or nodes from the tree that provide little or no additional information gain in the prediction of the target variable [55].