# Stability of Feature Selection in Multi-Omics Data Analysis
## 3 Results
The stability of feature selection values, as measured by the Nogueira metric, is summarized in Table 3 and Figure 3 for the examined classification methods across different ranges of the regularization parameter \(C\) (low, med, high). Among the classifiers evaluated, the SVM demonstrated varying stability, with the highest stability for the _mirna_ layer at the low \(C\) range, achieving a value of 0.597. However, stability decreased significantly in the high \(C\) range, with an overall stability score of only 0.353, indicating reduced reliability in feature selection. The LR exhibited consistent performance, particularly at the low \(C\) range, where the stability for the _mirna_ layer reached 0.590. Stability values for LR were generally lower in the med and high ranges, reflecting a consistent but less robust feature selection across the parameter spectrum. The Lasso regression also showed strong stability at the low \(C\) range, with the highest value of 0.589 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Classifier**} & \multicolumn{5}{c}{**Omics Layer**} \\  & **-ALL** & **cnv** & **mirna** & **mutation** & **ma** \\ \hline SVM\_low & 0.482 \(\pm\) 0.086 & 0.449 \(\pm\) 0.079 & **0.597 \(\pm\) 0.091** & 0.420 \(\pm\) 0.093 & 0.470 \(\pm\) 0.085 \\ SVM\_med & 0.396 \(\pm\) 0.035 & 0.381 \(\pm\) 0.039 & 0.470 \(\pm\) 0.047 & 0.398 \(\pm\) 0.045 & 0.387 \(\pm\) 0.035 \\ SVM\_high & **0.353 \(\pm\) 0.033** & **0.364 \(\pm\) 0.030** & 0.372 \(\pm\) 0.046 & **0.363 \(\pm\) 0.036** & **0.345 \(\pm\) 0.033** \\ LR\_low & 0.479 \(\pm\) 0.082 & 0.453 \(\pm\) 0.080 & **0.590 \(\pm\) 0.087** & 0.419 \(\pm\) 0.093 & 0.464 \(\pm\) 0.089 \\ LR\_med & 0.397 \(\pm\) 0.035 & 0.385 \(\pm\) 0.041 & 0.472 \(\pm\) 0.045 & 0.401 \(\pm\) 0.050 & 0.390 \(\pm\) 0.034 \\ LR\_high & 0.384 \(\pm\) 0.033 & 0.372 \(\pm\) 0.031 & 0.394 \(\pm\) 0.041 & 0.383 \(\pm\) 0.028 & 0.376 \(\pm\) 0.037 \\ Lasso\_low & 0.470 \(\pm\) 0.089 & 0.447 \(\pm\) 0.080 & **0.589 \(\pm\) 0.080** & 0.424 \(\pm\) 0.093 & 0.462 \(\pm\) 0.091 \\ Lasso\_med & 0.401 \(\pm\) 0.044 & 0.376 \(\pm\) 0.042 & 0.488 \(\pm\) 0.033 & 0.399 \(\pm\) 0.050 & 0.395 \(\pm\) 0.037 \\ Lasso\_high & 0.376 \(\pm\) 0.033 & 0.368 \(\pm\) 0.030 & 0.409 \(\pm\) 0.041 & 0.374 \(\pm\) 0.036 & 0.366 \(\pm\) 0.030 \\ \hline \hline \end{tabular} The best results are highlighted in green, while the weakest results are highlighted in red.  
\end{table} 
Table 3: The values of feature-selection stability (means and standard deviations), as measured by the Nogueira metric, obtained for the classification methods across three ranges of \(C\) parameter values (low, med, high). Figure 2: Classification accuracy values on the test part of the dataset achieved for the examined classification methods in the three ranges of \(C\) parameter values. The central dots represent the mean values calculated from the results across 15 datasets and 15 spits of each dataset. The vertical lines represent the standard deviation values. for the _minna_ layer. However, similar to the other methods, stability diminished in the higher parameter ranges, especially noted with a score of 0.366 for the _rna_ layer in the high range. Overall, the low \(C\) range consistently yielded better feature-selection stability across all classifiers, highlighting the trade-off between model complexity and stability in multi-omics data analysis. The weighted harmonic mean \(F_{\beta}\) of classification accuracy and feature-selection stability values, achieved for the examined classification methods across different ranges of the regularization parameter \(C\) (low, med, high), is summarized in Table 4. This measure provides a balanced assessment of both performance metrics, with equal weighting assigned (\(\beta=1\)). Among the classifiers, the LR achieved the highest overall weighted harmonic mean in the low \(C\) range, with a value of 0.575, indicating strong performance in both classification accuracy and feature-selection stability.