## 6 The Numerical Example  
In this section, we provide a numerical example to explain the proposed method, i.e., \"the proposed method simulation.\" Five samples from both classes A and B are shown in Tables 5 and 6, respectively. Then, the maximum and minimum values were extracted, and the mean values were calculated from the first five features in both classes shown in Tables 7-9, respectively. Features 1, 3, and 4 represented ideal cases, where we expanded the intervals and started to generate virtual random numbers based on a Gaussian distribution without any pre-processing, but Feature 2 was case H, so we performed a preprocessing before generating random numbers. In case H, to convert it to the ideal case, the MaxB or MinA would be changed depending on this simple comparison. **If (MeanA - MinA > MaxB - MeanB)**  
**MinA = next position in the list, which is sorted in ascending order; Else**  
**MaxB = next position in the list, which is sorted in descending order;**  
**End**  
The condition is false (3.28 - 3 > 3.2 - 2.92), so MaxB = 3.1; Check that the case is still not the ideal case; it is a case H; \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature 1** & **Feature 2** & **Feature 3** & **Feature 4** \\ \hline
7.000 & 3.2000 & 4.7000 & 1.4000 \\
6.4000 & 3.2000 & 4.5000 & 1.5000 \\
6.9000 & 3.1000 & 4.9000 & 1.5000 \\
5.5000 & 2.3000 & 4.0000 & 1.3000 \\
6.5000 & 2.8000 & 4.6000 & 1.5000 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Five samples from the first class (B). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature 1** & **Feature 2** & **Feature 3** & **Feature 4** \\ \hline MAX & 5.1000 & 3.6000 & 1.5000 & 0.2000 \\ MAX B & 7 & 3.2000 & 4.9000 & 1.5000 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The maximum values extracted from the first five features. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature 1** & **Feature 2** & **Feature 3** & **Feature 4** \\ \hline
7.000 & 3.2000 & 4.7000 & 1.4000 \\
6.4000 & 3.2000 & 4.5000 & 1.5000 \\
6.9000 & 3.1000 & 4.9000 & 1.5000 \\
5.5000 & 2.3000 & 4.0000 & 1.3000 \\
6.5000 & 2.8000 & 4.6000 & 1.5000 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The minimum values extracted from the first five features. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Feature 1** & **Feature 2** & **Feature 3** & **Feature 4** \\ \hline Mean A & 4.8600 & 3.2800 & 1.4000 & 0.2000 \\ Mean B & 6.4600 & 2.9200 & 4.5400 & 1.4400 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The mean values calculated from the first five features. a limited size. More specifically, when applied to the IRCCS Medea dataset, our method augmented the classification accuracy from 84.9 [35] to 95%, 83.8%-93.9% for only three samples in each class for the _E. coli_ dataset, and from 91.7%-100% for the Breast Tissue dataset. These findings demonstrated that our technique not only offered high classification accuracy, but was also reliable and easy to apply (refer to Algorithms 1 and 2). The experiments reported in this study also showed that, given an appropriate number of the generated virtual samples, the generalization efficiency of the classification on the new training set may be better than that of the original training set, and this agrees with many studies such as [34]. Future studies might delineate more specific matters in determining the best number for the original sample and the virtual sample in order to get maximum accuracy in terms of the results. In addition, the technique could be applied to a wide dataset to determine the strengths and limitations. These suggested directions could help to ensure that this important methodology is further and enhanced. [PERSON] conducted all experiments, analyses the results and wrote the first draft of the manuscript, [PERSON] provided data for the RCCSMedea dataset and revised the manuscript in each stage, [PERSON]-[PERSON] substantially contributed to the conception and design of the study, supervised and provided critical revision of the article.