## 4 Features Selection and Analysis
### Feature Selection  
A statistical analysis was conducted on the extracted features to select the most informative ones for use in the machine learning algorithms. This analysis, based on the methodology described in [41], is summarized in Figure 9. As an initial step, a one-way Analysis of Variance (ANOVA) test was applied to determine whether its residuals exhibit a normal distribution.  
To validate the normal distribution of residuals, we utilized the one-sample Kolmogorov-Smirnov, Anderson-Darling, and Lilliefors tests. The one-sample Kolmogorov-Smirnov test is used to compare the empirical distribution of our sample with a specified theoretical distribution by evaluating the maximum deviation between these distributions. The Anderson-Darling test, while similar in purpose to the Kolmogorov-Smirnov test, places greater emphasis on the tails of the distribution, enhancing sensitivity to tail differences between the empirical and theoretical distributions. Lastly, the Lilliefors test, a variant of the Kolmogorov-Smirnov test, specifically tests for normality by accommodating the estimation of mean and variance from the sample data, unlike the standard Kolmogorov-Smirnov test which assumes these parameters are known. The results indicated that while some features conform to a normal distribution, others do not. Consequently, to determine the \(p\)-values for each feature, we applied two different tests [42]. These are the Kruskal-Wallis test, which is appropriate when the ANOVA residuals do not exhibit normal distribution, and the ANOVA test, which is suitable when they do [43]. Features with p-values exceeding the threshold of 0.05 were discarded. Subsequently, we constructed a list prioritizing features; those with the lowest \(p\)-values were given the highest precedence.  
This statistical study was conducted for four distinct binary classification tests, each designed to examine the potential for distinguishing subjects based on specific characteristics: gender, age, BMI, and CWP. The objective of these tests is to facilitate binary classification according to predefined criteria for each characteristic.  
Figure 9: Statistical analysis diagram.  
- Male: 46 people;  
- 18-29 years old: 46 people;  
- 18-25 kg/m\({}^{2}\): 47 people;  
- \(\leq\)100 cm: 46 people;
- \(>\)100 cm: 46 people.  
After establishing a priority queue for each binary classification problem, a correlation matrix was constructed to further refine the feature selection [44]. This step helps identify features that contain redundant information, indicated by high correlation values. A feature was deemed highly correlated with others if the absolute value of the correlation exceeded 0.7. If the matrix indicates a correlation value equal to or higher than this threshold, the features in question are evaluated against the priority list. Only the feature with the highest priority is retained for subsequent analysis. Figure 10 graphically illustrates this process for the gender classification test. Figure 10 is a visual representation of the correlation matrix among features where a ball's size and color denote the correlation value, with larger balls (with a diameter equal to the square) indicating a correlation of 1 (red) or \(-1\) (blue). Contrariwise, smaller dot-represented balls represent a correlation near 0. This approach simplifies the analysis of correlations across a larger set of features, providing a more accessible interpretation of the correlation matrix.  
The features resulting from this process are those selected for use in the machine learning algorithms to classify the defined binary tests. The resulting features vary for each binary classification test, as presented in Table 4.