# Stability of Feature Selection in Multi-Omics Data Analysis
## 3 Results  
This section presents and discusses the results obtained from our experiments. The focus of this presentation will be on the three aspects investigated: classification accuracy, feature-selection stability, and our proposed metric, which combines classification accuracy and feature-selection stability into a single parameter. Given the large number of datasets used in this study, we will not present the results for each dataset individually. Instead, we will report averaged values and standard deviations for each type and kind of classifier studied, with a breakdown by omics layer. This approach will allow for more general conclusions to be drawn. The classification accuracy values for the examined methods across different omics layers are detailed in Table 2 and Figure 2. The results are categorized by three ranges of the regularization parameter \(C\) (low, med, high). It can be observed that for virtually every omics layer, the highest classification accuracy is achieved with classifiers of med-complexity. This suggests that moderate model complexity, defined by the number of features used, is optimal for achieving accuracy. Increasing or decreasing the number of features leads to a decline in classification accuracy. Regarding the classification accuracy values, the highest results were seen with the _ALL_ (0.721-0.745) and _rna_ (0.723-0.744) layers, while the lowest results were observed with the _mutation_ layer (0.605-0.617). \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Classifier**} & \multicolumn{5}{c}{**Omics Layer**} \\  & **—ALL\_** & **cnv** & **minra** & **mutation** & **ma** \\ \hline SVM\_low & 0.724 \(\pm\) 0.061 & 0.663 \(\pm\) 0.070 & 0.686 \(\pm\) 0.065 & 0.612 \(\pm\) 0.063 & 0.729 \(\pm\) 0.059 \\ SVM\_med & **0.743 \(\pm\) 0.061** & 0.678 \(\pm\) 0.064 & 0.685 \(\pm\) 0.063 & 0.616 \(\pm\) 0.056 & **0.740 \(\pm\) 0.062** \\ SVM\_high & 0.721 \(\pm\) 0.066 & 0.661 \(\pm\) 0.069 & 0.655 \(\pm\) 0.061 & **0.605 \(\pm\) 0.062** & 0.723 \(\pm\) 0.064 \\ LR\_low & 0.723 \(\pm\) 0.062 & 0.661 \(\pm\) 0.070 & 0.685 \(\pm\) 0.066 & 0.612 \(\pm\) 0.065 & 0.728 \(\pm\) 0.060 \\ LR\_med & 0.739 \(\pm\) 0.064 & 0.677 \(\pm\) 0.066 & 0.685 \(\pm\) 0.063 & 0.615 \(\pm\) 0.058 & 0.738 \(\pm\) 0.065 \\ LR\_high & 0.728 \(\pm\) 0.063 & 0.668 \(\pm\) 0.065 & 0.661 \(\pm\) 0.060 & **0.606 \(\pm\) 0.058** & 0.728 \(\pm\) 0.065 \\ Lasso\_low & 0.727 \(\pm\) 0.057 & 0.684 \(\pm\) 0.070 & 0.684 \(\pm\) 0.064 & 0.608 \(\pm\) 0.063 & 0.732 \(\pm\) 0.056 \\ Lasso\_med & **0.745 \(\pm\) 0.062** & 0.690 \(\pm\) 0.059 & 0.696 \(\pm\) 0.059 & 0.617 \(\pm\) 0.058 & **0.743 \(\pm\) 0.060** \\ Lasso\_high & 0.742 \(\pm\) 0.061 & 0.681 \(\pm\) 0.069 & 0.678 \(\pm\) 0.064 & **0.606 \(\pm\) 0.058** & **0.744 \(\pm\) 0.059** \\ \hline \end{tabular}  
* The best results are highlighted in green, while the weakest results are highlighted in red.  
\end{table} 
Table 2: Classification accuracy values (means and standard deviations) on the test part of the dataset achieved for the examined classification methods in the three ranges of \(C\) parameter values (low, med, high). Among the classifiers evaluated, the SVM model exhibited the highest overall accuracy at the med range of \(C\) with an accuracy of 0.743, while the weakest performance was observed for the mutation layer in the high range, with an accuracy of 0.605. The LR model exhibited slightly lower accuracy compared to SVM. However, similar to SVM, its best performances (0.739 and 0.738) were achieved in the med range. The achieved peak accuracies of 0.745 in the med range for the overall dataset and 0.743 for the _rna_ omits layer, highlighting its effectiveness in this configuration. It is also worth noting that the differences in classification accuracy across classifier types (SVM, LR, Lasso) in corresponding configurations are minimal.