## 3 Materials and Methods
### Data Preprocessing
#### 3.2.2 Dimensional Operations  
As datasets increase in size, either through the number of predictor variables or the number of samples, data mining algorithms face a dimensionality problem. This issue significantly raises computational costs and can hinder the performance of many data mining algorithms. It can be solved by feature selection (FS)- and space transformation-based methods.  
* **Feature Selection:** Feature selection is defined as the process of obtaining a subset from an original feature set based on certain feature selection criteria that select the relevant features from the dataset. It compresses the data processing scale by eliminating unnecessary and irrelevant features. Feature selection algorithms are divided into three classes: filter-based, wrapper, and embedded. Filter-based approaches evaluate the performance of a particular machine learning algorithm according to the value of each feature without considering it. They select features from the dataset according to the relationships between the data. Wrapper methods, on the other hand, iteratively train the algorithm using a subset of features. Features are added and removed based on the results obtained from the training prior to modeling. Stopping criteria for selecting the best subset, such as a decrease in model performance or reaching a predetermined number of features, are typically defined in advance by the model trainer. Embedded methods integrate the feature selection process as part of the learning algorithm itself, incorporating built-in feature selection techniques. These methods address the disadvantages of both filter and wrapper methods while combining their advantages [41].  
The filter-based feature selection algorithms used in this study are summarized below:  
**ANOVA F-Test**: Analysis of variance, or ANOVA. A statistical method called the F-test is used to assess whether the means of three or more independent groups differ in ways that are statistically significant. The F-statistic is used to assess the ratio of within-group variability to between-group variability. By determining whether the means of a numerical feature vary significantly among the target variable's categories, ANOVA can be used in feature selection to evaluate the association between a categorical target variable and numerical predictor features [42; 43].  
**Mutual Information:** This method measures whether two variables are mutually dependent, providing insight into the amount of information obtained for one variable when the other is observed. It measures the contribution of a feature to the target prediction based on the presence/absence of that feature.  
**Chi-square Test**: In statistics, the chi-square test is used to test the independence of two events. Given the data of two variables, it calculates the observed count (\(O\)) and the expected count (\(E\)). Chi-square measures how the expected count E and the observed count O deviate from each other.  
\[X_{c}^{2}=\sum\frac{(O_{i}-E_{i})^{2}}{E_{i}} \tag{1}\]  
where, \(c\), is the degree; \(O\), is the observed value(s); \(E\), is the expected value(s).  
* **Space Transformations:** Space transformation techniques, instead of selecting the most promising features, combine the original features to create a completely new set of features. Such a combination can be made based on various criteria. Principal component analysis (PCA) is one of the most commonly used methods for this purpose [44].