## 4 Results  
For a relevant analysis of feature selection, the first step consists of classification with all available features in the database. Thus, for this, we tested all the classifiers available in MATLAB with the original data from the two databases used. Then, we compared the results with those obtained after applying feature selection both with selection methods available in the MATLAB environment and with selection methods based on the sparsity principle, a principle that is also used in compressed sensing or even in the selection of relevant states (LASSO and Group LASSO). Figure 1 shows the results obtained with the arrhythmias database. It can be observed that, for the classification of the 13 classes, the best classification rate is that obtained with an ensemble of bagged trees classifiers, namely, a classification of 74.8% (for five-fold cross-validation). This database has a strongly unbalanced nature in terms of the data distribution across the 13 classes. Table 3 presents the classification results for the case where the most important features are selected using different feature selection methods available in the APP Machine Learning environment in MATLAB. This APP provides several methods, which have been tested on the two datasets and will be briefly presented below. Minimum redundancy maximum relevance (MRMR) works by combining two main criteria: the maximum relevance and the minimum redundancy. Its goal is to select a subset of features that are both highly relevant to the target variable and as uncorrelated with each other as possible. The chi-square test (CHI2) measures the independence between each feature and the target class, acting as a statistical association test. ANOVA performs an ANOVA test for each feature to determine whether the feature values differ significantly between groups defined by the class labels. Features with \(p\)-values below a stability threshold are selected for use in the machine learning model. The Kruskal-Wallis test is a nonparametric alternative to one-way ANOVA. Instead of using the F-statistic from classic ANOVA, the Kruskal-Wallis test employs a chi-square statistic, with the significance being determined by a \(p\)-value. Figure 1: Classification results with multiple classifiers for arrhythmias database for all features in the database and the confusion matrix for the best performing classifier. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Arrhythmia Database from UCI Machine Learning Repository [29]** \\
**452 Instances Grouped into 13 Classes, with 279 Features for Each Instance** \\ \hline \hline \multicolumn{3}{c}{**No. of Features**} & **Classification Rate** \\ \hline \multicolumn{3}{c}{**Original Data OR Method of Feature Selection**} \\ \hline ORIGINAL DATA \({}^{*}\) & **279** & **74.8** \\ \hline MRMR & 50 & 71.7 \\  & 100 & 74.6 \\  & 125 & 75 \\ \hline CHI2 & 50 & 73.7 \\  & 100 & 73.2 \\  & 150 & 73.9 \\ \hline ANOVA & 50 & 74.8 \\  & 100 & 72.6 \\  & 150 & 74.6 \\ \hline KRUSKAL WALLIS \({}^{*}\) & **50** & **75.7** \\  & **100** & **73** \\  & **150** & **75.9** \\ \hline LS & 50 & 65.3 \\  & 100 & 69.9 \\  & 150 & 72 \\ \hline ReliefF & 50 & 64.6 \\  & 100 & 69.7 \\  & 150 & 71.7 \\ \hline \hline \end{tabular} \({}^{*}\)The results for original data and the best results for feature selections are written in bold.  
\end{table} 
Table 3: Classification results for arrhythmia database with all data and feature selection results using standard methods in MATLAB Machine Learning APP. The least squares (LS) algorithm for feature selection is based on solving a system of equations by minimizing the error between the predicted and actual values (in regression problems). This algorithm is typically used in linear regression or similar methods to select the most relevant features that contribute to reducing the model error. ReliefF (relief for feature selection) is an algorithm used for feature selection based on the importance of the features in their classification.