## 4 Results
It is an improved version of the relief algorithm, offering greater robustness in multi-class datasets. Figure 2 exemplifies the importance of features obtained with different feature selection methods. It is found that, when applying different feature selection methods, other features are found to be relevant or their importance differs depending on the method applied. In Table 3, it can be observed that, using all available features from the arrhythmia dataset, the best classification rate achieved with an ensemble of bagged trees classifiers using five-fold cross-validation is 74.9%. When selecting only the most relevant features, the classification rate decreases slightly, but depending on the number of selected features and the selection method, the results remain comparable or are even improved. As seen in Table 3, using the Kruskal-Wallis method for feature selection, it is possible to achieve improved results while keeping only 50 features. For the above, this method yields the best classification results while significantly reducing the number of selected features. If the goal is to minimize the number of selected features for classification (e.g., when hardware resources or the classification time is crucial), all tested methods prove suitable, and the classification results remain comparable to those obtained using the full dataset. For the case of using feature selection methods based on the sparsity of the signal, methods closely related to compressed sensing and the sparse representation of a signal, the results are presented in Table 4. It is noted that the feature selection method based on the alternating direction method of multipliers (BP_ADMM) leads to improved classification results (77%) for selecting the most important 248 features. However, the LASSO, group LASSO, and OMP methods also provide classification rates comparable to the initial space. The weakest results are obtained when using random projections, which is the first part of the compressed sensing method. This first part does not involve the aspects related to the sparsity of the signal. These weaker results might also be due to the uneven distribution of data across the 13 classes. Figure 2: The importance of features with different feature selection algorithms from filtered methods. Figure 3 exemplifies the importance of features obtained by different feature selection methods. It is found that their importance differs depending on the method applied and, by applying a threshold, relevant features are selected. The choice of threshold is an empirical matter, which depends on the database or the number of desired features. Figure 4 shows the results obtained with oncological databases with all data using the standard classifiers from APP Machine Learning. It has been found that, using all 4000 features, a maximum classification rate of 98.6% is obtained. Figure 5 exemplifies the importance of features obtained with different feature selection methods from the oncological databases. It is found that, for the ADMM algorithm, very few features are significant, with the importance of others being insignificant or even null. In the case of the group LASSO method, a threshold must be applied to find significant features because the algorithm fails to produce sparsity in the feature importance vector. \begin{table}
\begin{tabular}{l l l} \hline \hline  & **No. of Features** & **Classification Rate** \\ \hline
**ORIGNAL DATA \({}^{*}\)** & **279 features** & **74.8\%** \\ CS\_RandomProjections & 100 features & 59.5\% \\ Lasso & 72 features & 73.2\% \\ GroupLasso & 142 features & 69\% \\ OMP with no. feature setting & 100 features & 73.2\% \\
**BP\_ADMM \({}^{*}\)** & **248 features** & **77\%** \\ \hline \hline \end{tabular} \({}^{*}\)The results for original data and the best results for feature selections are written in bold.  
\end{table} 
Table 4: Classification results for arrhythmia database for feature selection using signal sparsity-based methods.