## 2 Methods
### KNN-Is and SMOTE in Big Data
Table 5 summarizes the average ranks of each strategy based on the Friedman test, where the strategy with the best performance obtains the lowest rank, and the worst-performing approach receives the highest rank [48]. According to the results, \(D_{d_{p}}\)+SMOTE ranked the best overall, with an average rank of 1.1, indicating that it consistently outperformed the other strategies across the different datasets. SMOTE was ranked second with an average rank of 2. The imbalanced strategy ranked third, and finally, \(D_{d_{p}}\), obtained the highest average rank, indicating that it was the worst-performing strategy. Based on the Iman and Davenport statistic \(F_{F}\), distributed according to the \(F\) distribution with four algorithms and nine datasets, yielding a value of 31.512, and a computed \(p\)-value of 0.00000017243, we reject the null hypothesis at the significance level of \(\alpha=0.05\). This indicates that there are significant differences among the algorithms tested. Further analysis using the Bonferroni-Dunn's procedure as a post hoc method is presented in Table 6, showing the \(p\)-values obtained over the results of the Friedman test with \(\alpha=0.05\), using \(D_{d_{p}}\)+SMOTE as the control algorithm. With a \(p\)-value of 0.016667, we reject the null hypothesis for the following pairs, indicating that the control algorithm is superior: \(D_{d_{p}}\)+SMOTE vs. Ddp and \(D_{d_{p}}\)+SMOTE vs. Imbalanced. However, there is no significant difference between \(D_{d_{p}}\)+SMOTE vs. SMOTE, suggesting that they perform similarly well. \begin{table}
\begin{tabular}{l c c c c c c c} \hline
**Name** & **Dataset** & \(p\) & **Features** & **TPR** & **TNR** & **AUC** & \(G-mean\) \\ \hline Imbalanced & & – & 24,832 & 0.44767 & 0.99177 & 0.71972 & 0.66633 \\ SMOTE & & 2.00 & 24,832 & 0.78488 & 0.91916 & 0.85202 & 0.84937 \\ \cline{3-8}  & & 0.33 & 2000 & 0.31395 & 0.99325 & 0.65360 & 0.55842 \\ \(D_{d_{p}}\) & NewIndian12 & & 0.33 & 1000 & 0.30233 & 0.99341 & 0.64872 & 0.54803 \\ \(D_{d_{p}}\) + SMOTE & & 0.50 & 500 & 0.95612 & 0.76943 & 0.86723 & 0.86169 \\  & & 0.25 & 1000 & 0.91279 & 0.81017 & 0.86148 & 0.85995 \\ \hline Imbalanced & & – & 24,832 & 0.54959 & 0.96886 & 0.75740 & 0.72728 \\ SMOTE & & 2.00 & 24,832 & 0.85676 & 0.91797 & 0.88736 & 0.88684 \\ \(D_{d_{p}}\) & NewIndian14 & & 0.25 & 1000 & 0.36486 & 0.98434 & 0.67460 & 0.59929 \\  & & 0.25 & 100 & 0.37027 & 0.97294 & 0.76161 & 0.60021 \\ \(D_{d_{p}}\) + SMOTE & & 1.00 & 10 & 0.97838 & 0.85160 & 0.91499 & 0.91279 \\  & & 2.00 & 1000 & 0.96486 & 0.86266 & 0.91376 & 0.91233 \\ \hline Imbalanced & & – & 24,832 & 0.08838 & 0.99445 & 0.53141 & 0.26076 \\ SMOTE & & 2.00 & 24,832 & 0.67521 & 0.84909 & 0.76255 & 0.75754 \\ \(D_{d_{p}}\) & NewIndian15 & & 0.50 & 2000 & 0.02564 & 0.99835 & 0.51209 & 0.16001 \\  & & 0.50 & 1000 & 0.02564 & 0.99788 & 0.51176 & 0.15996 \\ \(D_{d_{p}}\) + SMOTE & & 0.33 & 2000 & 0.91453 & 0.71888 & 0.81670 & 0.81082 \\  & & 0.50 & 10 & 0.94872 & 0.68364 & 0.81618 & 0.80534 \\ \hline \end{tabular}
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{c c} \hline
**Algorithm** & **Ranking (AUC)** \\ \hline Imbalanced & 3.3 \\ SMOTE & 2 \\ \(D_{d_{p}}\) & 3.6 \\ \(D_{d_{p}}\)+SMOTE & 1.1 \\ \hline \end{tabular}
\end{table} 
Table 5: Average rankings of the algorithms (Friedman) using _AUC_. ## 5 Conclusions

The motivation for this study lies in addressing significant challenges encountered in Big Data analytics, specifically class imbalance, high dimensionality, and class overlapping. In this paper, we propose a hybrid approach based on several data-level solutions for addressing the class imbalance problem in Big Data datasets with high dimensionality. The proposal combines a dissimilarity approach to transform the datasets into a low-dimensional space using fractional norms and the well-known SMOTE technique. This strategy can improve the quality of the data by reducing the dimensionality and balancing the classes.