## 2 Method Description
### The Second Phase of the Proposed Method
The p-values for the comparisons \(a=0.001\) vs. \(a=0.005\) (\(p=0.75\)), \(a=0.001\) vs. \(a=0.01\) (\(p=0.41\)), and \(a=0.005\) vs. \(a=0.01\) (\(p=0.94\)) indicate the absence of statistically significant differences. This shows that the choice of parameter \(a\) does not significantly influence the model's performance on the regression datasets. \begin{table}
\begin{tabular}{c c c c} \hline
**Dataset** & \(a=0.001\) & \(a=0.005\) & \(a=0.01\) \\ \hline Abalone & 5.10 & 5.12 & 5.10 \\ \hline Airfoil & 0.004 & 0.004 & 0.004 \\ \hline Auto & 9.68 & 9.80 & 9.89 \\ \hline Baseball & 86.19 & 77.46 & 81.97 \\ \hline BK & 0.153 & 0.043 & 0.11 \\ \hline BL & 0.0002 & 0.0002 & 0.0003 \\ \hline Concrete & 0.006 & 0.006 & 0.006 \\ \hline Dee & 0.16 & 0.16 & 0.16 \\ \hline Housing & 18.70 & 18.73 & 19.20 \\ \hline Friedman & 1.45 & 1.44 & 1.45 \\ \hline FA & 0.019 & 0.09 & 0.07 \\ \hline FY & 0.077 & 0.12 & 0.076 \\ \hline HO & 0.01 & 0.01 & 0.01 \\ \hline Laser & 0.003 & 0.003 & 0.003 \\ \hline MB & 5.49 & 0.56 & 0.48 \\ \hline Mortgage & 0.14 & 0.12 & 0.13 \\ \hline NT & 0.007 & 0.007 & 0.007 \\ \hline PL & 0.023 & 0.023 & 0.023 \\ \hline Plastic & 2.29 & 2.29 & 2.29 \\ \hline PY & 0.019 & 0.019 & 0.017 \\ \hline Quake & 0.036 & 0.036 & 0.036 \\ \hline SN & 0.024 & 0.025 & 0.024 \\ \hline Stock & 1.53 & 1.52 & 1.52 \\ \hline Treasury & 0.51 & 0.54 & 0.47 \\ \hline
**Average** & **5.48** & **4.92** & **5.13** \\ \hline \end{tabular}
\end{table} 
Table 5: Experimental results for regression datasets using different values for parameter \(a\). ### Experiments on the Parameter F

Another experiment was conducted using the initialization factor \(F\). Table 6 presents the percentage error rates of the proposed machine learning model across various classification datasets for four different values of the parameter \(F\) (1.5, 3.0, 5.0, 10.0). Analyzing the data reveals that the parameter \(F\) influences the model's performance, but this effect varies by dataset. The lowest average error rate is observed for \(F=5.0\) (18.58%), indicating that this value is generally optimal. For the other values, slightly higher average error rates are noted: 18.88% for \(F=3.0\); 18.67% for \(F=10.0\); and the highest rate, 20.32%, for \(F=1.5\). Examining individual datasets, it is evident that for many of them, increas

Figure 8: Statistical comparison of the obtained results from the application of the current method on the classification datasets using different values of perturbation factor \(a\). Figure 9: Statistical comparison of the obtained experiments results from the application of the proposed method to the regression datasets, using different values of the perturbation factor \(a\). ing \(F\) improves performance, as reflected in reduced error rates. Examples include the \"Ionosphere\", \"Wine\", and \"ZONF_S\" datasets, where error rates decrease as \(F\) increases. On \"Ionosphere\", the error rate drops from 12.92% for \(F=1.5\) to 7.39% for \(F=10.0\). On \"Wine\", the error rate decreases from 10.90% for \(F=1.5\) to 7.71% for \(F=10.0\). Similarly, on \"ZONF_S\", the error rate steadily decreases from 2.59% for \(F=1.5\) to 1.79% for \(F=10.0\). However, there are cases where increasing \(F\) does not lead to improvement or results in higher error rates. For example, on the \"Segment\" dataset, the error rate rises from 35.81% for \(F=1.5\) to 40.83% for \(F=10.0\). On the \"Spiral\" dataset, the error rate consistently increases from 13.28% for \(F=1.5\) to 22.52% for \(F=10.0\). A similar trend is observed on the \"Z_O_N_F_S\" dataset, where the error rate rises from 46.00% for \(F=1.5\) to 46.77% for \(F=10.0\). Overall, the parameter \(F\) significantly affects the model's performance, and the optimal value appears to be \(F=5.0\), as evidenced by the lowest average error rate. However, the exact impact depends on the characteristics of each dataset, emphasizing the need to fine-tune the parameter value for specific datasets to achieve optimal performance.