# Leveraging Feature Extraction to Perform Time-Efficient Selection for Machine Learning Applications
## 4 Computational Study
Despite low R\({}^{2}\) values, the statistical significance of the models ensures that the identified relationships are meaningful within the context of the analysis. Additionally, any conclusions derived from these models will later be compared to other analysis approaches, such as graphical analysis and two-tailed \(t\)-tests, to reinforce the robustness and consistency of the findings. Focusing on the different dependent variables, some conclusions may be reached. Through comparison of coefficients relative to Group[T.Proposed] for precision, recall, and f-beta, it is clear that PM does not readily match the performance achieved by other approaches. This conclusion is very significant (\(\alpha=0.05\geq p\) value) for all the cases presented. Counteracting the last point, the effect of the target feature set length (combination length) appears to impact the various dependent variables positively specifically for PM. This conclusion approaches significance for all cases except one, which means it is significant (\(\alpha=0.1\geq p\) value). The exception occurs for weighted precision in the case of multiclassification in which the relevant \(p\)-value is equal to 0.187, which means the calculated coefficient is only relevant for approximately 80% of cases. The observations exposed above are largely reiterated when analyzing the results obtained for the \(t\)-tests across the two groups (Table 10). Taking into account weighted precision, weighted recall, and weighted F-beta, it is possible to conclude that the difference between the two groups, seems to become smaller and less relevant the more the combination length increases. This conclusion is reached since the test statistic (z) for these cases tends to decrease in absolute value, which denotes a smaller difference, and the \(p\)-value on the other hand tends to increase, which allows for a stronger assurance relative to the methods null hypothesis; in this case \(H_{0}:\mu 1=\mu 2\), meaning the difference between the two groups becomes less clear. These conclusions are consistent with the behavior observed in Figures 13-18. Concerning the elapsed time, in all cases, it is apparent that the PM is significantly faster than other solutions. This is observable through the coefficient values present for Group[T.Proposed]. This conclusion stands as strongly significant both for binary and multi-class classification, since \(\alpha=0.05\geq p\) value, as observed in Tables 8 and 9. Additionally, the target feature set length appears to have little impact in regards to the PM, as may be observed through the confidence values for CombLength:Group[T.Proposed] on those same tables, as well as their \(p\)-values, which do not allow for a reasonable significance level. Another conclusion one may make, although secondary, is that the group composed of other approaches is more affected by an increase in the elapsed time caused by an increase in the target feature set length; this may be interpreted through the difference between the value and the significance seen between the coefficients for CombLength and CombLength:Group[T.Proposed] in both cases. The same conclusion may be reached through consultation of Table 10, in which, no matter the combination length or task type involved, there appears to be a clear difference between the two groups. This is denoted by the very low \(p\)-values and the negative values presented for the test statistic (z), which indicate an advantage for the proposed method regarding computational speed. This significant difference may be further observed by checking the confidence intervals involved in this dependent variable's case. These conclusions are, as above, consistent with the behavior demonstrated in Figures 19 and 20. Due to computational cost constraints, the method was not evaluated on datasets containing thousands of features. However, an analysis of descriptive statistics from datasets with 90 or more features indicates that the proposed approach remains competitive even at higher dimensionalities.