## 3 Materials and Methods
### Methods  
For feature selection, we compared the classical methods from the MATLAB Classification Learner toolbox with some commonly used methods in compressed sensing. We conducted a comparative analysis of the results to see if the concept of sparsity from compressed sensing can be adapted for feature selection. In the case of databases where the data are not evenly distributed between classes, increased attention should be paid to the partition of data between the training and testing phases and the interpretation of the classification results. Thus, since the arrhythmia database is strongly unbalanced in the distribution of data between the 16 classes, we opted to report the classification rate and the confusion matrix for the highest classification rates for the classification variant with all features. In all classifications, we opted to use stratified cross-validation to avoid overtraining. Thus, for the classic feature selection approach, we used the algorithms available in MATLAB, namely, minimum redundancy maximum relevance (MRMR), the \(\chi^{2}\) test (CHI2), analysis of variance (ANOVA), the Kruskal-Wallis test, least squares (LS), and ReliefF. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Arrhythmia from UCI Machine Learning Repository**[29] & & \\
**452 Instances Grouped into 13 Classes, with 279 Features for Each Instance, of Which** \\
**206 Features Are Linear Value Attributes and the Rest Are Nominal Attributes.** & \\ \hline Class Number & Pathology & **Number of Instances** \\ \hline Class 1: & Normal & 245 \\ Class 2: & Ischemic changes (Coronary Artery Disease) & 44 \\ Class 3: & Old Anterior Myocardial Infarction & 15 \\ Class 4: & Old Inferior Myocardial Infarction & 15 \\ Class 5: & Sinus tachycardia & 13 \\ Class 6: & Sinus bradycardy & 25 \\ Class 7: & Ventricular Premature Contraction (PVC) & 3 \\ Class 8: & Supraventricular Premature Contraction & 2 \\ Class 9: & Left bundle branch block & 9 \\ Class 10: & Right bundle branch block & 50 \\ Class 11: & 1. degree AtrioVentricular block & 0 \\ Class 12: & 2. degree AtrioVentricular block & 0 \\ Class 13: & 3. degree AtrioVentricular block & 0 \\ Class 14: & Left ventricle hypertrophy & 4 \\ Class 15: & Atrial Fibrillation or Flutter & 5 \\ Class 16: & Others & 22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The data distribution from the arrhythmia database. In addition to these classical feature selection techniques, we also used concepts based on minimizing the L1 norm of the coefficients corresponding to the features. This concept is borrowed from the compressed sensing technique. The concept of compressed sensing (CS) and the LASSO feature selection algorithm share a common foundation in utilizing sparsity and L1 regularization to select a small subset of significant features from data. While CS focuses on reconstructing a signal from incomplete data, the LASSO algorithm is primarily concerned with feature selection in a predictive modeling context (regression or classification). These two concepts--compressed sensing and feature selection--have several similarities but also key differences. Next, we will highlight the main similarities and distinctions between these two techniques. The similarities between the two methods lie in several key aspects. Both are based on the idea of sparse representation, meaning they aim to select only a small subset of relevant features from all available ones. Both the LASSO and compressed sensing (CS) methods favor solutions where the coefficients for many features are zero. Additionally, both methods use a regularization term that penalizes large coefficients, employing the L1 norm to promote sparse solutions. Furthermore, both involve formulating linear optimization problems, which are solved using numerical methods that incorporate specific norms for constraints. The differences between the two methods lie in their primary purposes.