# Stability of Feature Selection in Multi-Omics Data Analysis
## 3 Results
The best stability was recorded for the _minna_ layer, reaching 0.632, which highlights the robustness of LR in this context. The SVM also performed well in the low \(C\) range, with a weighted harmonic mean of 0.578, demonstrating solid classification accuracy, particularly for the _minna_ layer at 0.637. However, performance decreased in the med and high ranges, suggesting that increasing model complexity adversely affects the balance between accuracy and stability. The Lasso regression \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Classifier**} & \multicolumn{5}{c}{**Omics Layer**} \\  & **-ALL\_** & **cnv** & **minra** & **mutation** & **ma** \\ \hline SVM\_low & 0.578 \(\pm\) 0.096 & 0.528 \(\pm\) 0.062 & **0.637 \(\pm\) 0.093** & 0.495 \(\pm\) 0.092 & 0.570 \(\pm\) 0.094 \\ SVM\_med & 0.515 \(\pm\) 0.049 & 0.485 \(\pm\) 0.049 & 0.553 \(\pm\) 0.043 & 0.482 \(\pm\) 0.054 & 0.507 \(\pm\) 0.048 \\ SVM\_high & 0.473 \(\pm\) 0.044 & 0.466 \(\pm\) 0.036 & 0.471 \(\pm\) 0.040 & **0.452 \(\pm\) 0.044** & **0.465 \(\pm\) 0.044** \\ LR\_low & 0.575 \(\pm\) 0.093 & 0.530 \(\pm\) 0.063 & **0.632 \(\pm\) 0.090** & 0.494 \(\pm\) 0.093 & 0.565 \(\pm\) 0.097 \\ LR\_med & 0.515 \(\pm\) 0.050 & 0.488 \(\pm\) 0.050 & 0.555 \(\pm\) 0.041 & 0.483 \(\pm\) 0.059 & 0.509 \(\pm\) 0.049 \\ LR\_high & 0.502 \(\pm\) 0.051 & 0.475 \(\pm\) 0.039 & 0.490 \(\pm\) 0.037 & 0.468 \(\pm\) 0.043 & 0.495 \(\pm\) 0.051 \\ Lasso\_low & 0.570 \(\pm\) 0.099 & 0.535 \(\pm\) 0.065 & **0.632 \(\pm\) 0.091** & 0.496 \(\pm\) 0.093 & 0.565 \(\pm\) 0.099 \\ Lasso\_med & 0.520 \(\pm\) 0.059 & 0.484 \(\pm\) 0.048 & 0.572 \(\pm\) 0.046 & 0.482 \(\pm\) 0.057 & 0.515 \(\pm\) 0.052 \\ Lasso\_high & 0.498 \(\pm\) 0.046 & 0.475 \(\pm\) 0.037 & 0.507 \(\pm\) 0.039 & **0.461 \(\pm\) 0.046** & 0.489 \(\pm\) 0.045 \\ \hline \hline \end{tabular} The best results are highlighted in green, while the weakest results are highlighted in red.  
\end{table} 
Table 4: Values (means and standard deviations) of the weighted harmonic mean \(F_{\beta}\) of classification accuracy and feature-selection stability achieved for the examined classification methods in the three ranges of \(C\) parameter values (low, med, and high). The values presented in the table were determined for \(\beta=1\), indicating equal weighting of classification accuracy and feature-selection stability. Figure 3: The values of feature-selection stability, according to the Nogueira measure, obtained for the tested classification methods across three ranges of \(C\) parameter values. The central dots represent the mean values calculated from the results across 15 datasets. The vertical lines represent the standard deviation values. exhibited similar trends, with the best overall performance in the low \(C\) range at 0.570 and notable stability for the _mirna_ layer at 0.632. As with the other methods, a decline in performance was observed as \(C\) increased, particularly evident in the high \(C\) range, where [PERSON] achieved the lowest score of 0.498. Overall, the results indicate that lower values of \(C\) tend to yield better balances between classification accuracy and feature selection stability across all classifiers, emphasizing the importance of model tuning in multi-omics analyses. Figure 4 presents a summary of the \(F_{\beta}\) values obtained for the three different \(\beta\)-weight values. In each case, the less-complex models (low, using fewer features) exhibit higher \(F_{\beta}\) values, even when the contribution of classification accuracy is weighted five times higher than feature-selection stability. Figure 4: Values of the weighted harmonic mean \(F_{\beta}\) of classification accuracy and feature selection stability achieved for the tested classification methods in the three ranges of \(C\) parameter values. The central dots represent the mean values calculated from the results across 15 datasets. The vertical lines represent the standard deviation values.