# Leveraging Feature Extraction to Perform Time-Efficient Selection for Machine Learning Applications
## 4 Computational Study
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Dep. Variable:** & \(R^{2}\) & **Adj. \(R^{2}\)** & \(F\) & \(\text{Pr}(F)\) & \(\text{log}\,L\) & \\ \hline Elapsed Time & \(0.119\) & \(0.114\) & \(98.98\) & \(4.80\times 10^{-51}\) & \(-2758.5\) & \\ \hline  & \(\hat{\beta}\) & **SE** & \(z\) & \(\text{Pr}(>|z|)\) & **[0.025** & **0.975**] \\ \hline
**Intercept** & \(27.3267\) & \(7.354\) & \(3.716\) & \(0.000\) & \(12.913\) & \(41.740\) \\
**CombLength** & \(3.5696\) & \(2.003\) & \(1.782\) & \(0.075\) & \(-0.356\) & \(7.495\) \\
**Group[T.Proposed]** & \(-33.3802\) & \(7.859\) & \(-4.247\) & \(0.000\) & \(-48.784\) & \(-17.976\) \\
**CombLength:Group[T.Proposed]** & \(0.1718\) & \(2.253\) & \(0.076\) & \(0.939\) & \(-4.244\) & \(4.588\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: GLS statistics for weighted recall in multi-class classification. outliers referring to combination lengths of 2 under binary classification. This may be caused due to the datasets provided for testing in this context not being well represented by a small amount of features in most cases according to these methods' approach. In Figures 5-10, the most clear trend present across the various plots is the improvement in performance of the PM as the length of the target feature set (combination_len) increases. The same trend seems to be visible in other methods such as EO and WOA, although it is less pronounced and more subtle. Through observation, it seems clear that PM lacks performance in smaller target set lengths; however, it rapidly catches the other methods with respect to performance when allowed to work with greater ones, even competing with most other feature selection methods. The loss in performance between binary and multi-classification tasks should also be pointed out. This decrease in performance is expected as multi-class classification is a distinctly more difficult task when compared to binary classification. In Figures 11 and 12, it is possible to observe the elapsed time distribution for each feature-selection method. It is important to note that due to how these other methods work (i.e., an agent-based architecture that has multiple agents search a solution space), a correction is taken into account regarding the max number of iterations and agents available for each one. This means that if, for example, the BBA method took 20,000 s in each of its tasks, the correct time to be compared to the PM would be as follows: 20,000 s/30 agents/50 iterations. This correction is applied to each data point collected from methods other than the PM. Despite that, as is observable, the PM still seemingly outperforms the other methods in all cases. Turning to the results pertaining to the two grouped division depicted in Figures 13-20. The overall conclusion from observing these plots matches those from the previous steps where other approaches were separate. The direct relation between the PM's performance and the length of the target feature is still apparent. A clear difference is visible between the PM and other solutions; however, the more the target set grows the more both groups approach each other, while maintaining a significant disparity in computational time. These inferences may be further examined by resorting to the coefficients presented in Tables 2-9. By analyzing the coefficients present in the GLS models represented in these tables, some conclusions can be drawn. Firstly, it is possible to reject the null hypothesis associated with the F-statistic for each GLS model--that is, the hypothesis that the independent variables and their interactions do not affect the dependent variable. This rejection is supported by the very low \(p\)-values (all below a significance threshold of \(\alpha=0.05\), corresponding to a 95% confidence level). It is important to note, however, that the primary objective of these GLS models is not to achieve strong predictive power, but rather to explore and analyze the relationships between the independent variables and the dependent variable.