## 4 Experimental Design
### Algorithm Comparison Experiments  
In this subsection, we compare HSDW-MI on 10 synthetic and 3 real data streams with other state-of-the-art algorithms that all of them can learn from multi-class data streams. LB [21], ARF [23], BOLE [25], and OAUE [28] are the online ensemble algorithms, which have concept drift detection mechanism and are mainly used to detect and solve drift problems. MUOB, MOOB [2], and CALMID [24] are ensemble algorithms with imbalance handling mechanism and are able to handle data streams with varying class ratio. The default parameters of all algorithms are set to \(D=2000\), \(N=20\), and the ensemble update threshold \(\theta\) of HSDW-MI is set to 0.5. Each comparison algorithm is evaluated by using four metrics, including macro-Recall, G-mean, macro-Precision, and macro-Fl-score. The results of the algorithm performance are shown in Tables 5-8. The results of the algorithm with the best performance are highlighted in bold. \begin{table}
\begin{tabular}{l l c c c c c c c c} \hline \hline \multirow{2}{*}{**Data Stream**} & \multicolumn{6}{c}{**Algorithm**} \\ \cline{2-10}  & & **LB** & **OAUE** & **ARF** & **BOLE** & **MUOB** & **MOOB** & **CALMID** & **HSDW-MI** \\ \hline \multirow{4}{*}{\begin{tabular}{l} Stationary data \\ stream \\ \end{tabular} } & ImbSta\_Stream & 96.44(3) & 94.45(6) & 96.70(2) & 94.96(5) & 82.52(8) & 94.22(7) & 96.06(4) & **97.21(1)** \\  & ImbSta\_Extreme\_Stream & 93.61(5) & 92.14(6) & 95.36(2) & 91.17(7) & 71.74(8) & 94.40(4) & 94.85(3) & **97.13(1)** \\  & ImbSta\_SG & 90.40(4) & 89.07(5) & 80.08(6) & 78.13(8) & 85.64(7) & 91.09(2) & **91.99(1)** \\  & ImbSta\_Extreme\_SG & 88.19(3) & 83.25(6) & 88.13(4) & 79.18(7) & 66.05(8) & 83.67(5) & 90.85(2) & **92.25(1)** \\  & ImbSta\_Extreme\_SIG & 84.97(4) & 80.75(6) & 88.54(3) & 77.45(7) & 63.63(8) & 81.82(5) & 88.76(2) & **92.18(1)** \\ \hline \multirow{4}{*}{\
\begin{tabular}{l} Variable data \\ stream \\ \end{tabular} } & ImbVar\_Stream & 76.00(8) & 91.75(4) & 91.50(5) & 92.02(3) & 87.57(6) & 92.11(2) & 86.50(7) & **92.64(1)** \\  & ImbVar\_Extreme\_Stream & 90.61(4) & 90.84(3) & 90.47(5) & 90.17(7) & 71.06(8) & 90.40(6) & 91.97(2) & **92.59(1)** \\  & ImbVar\_SG & 91.45(4) & 89.26(5) & 91.82(3) & 87.17(7) & 78.01(8) & 85.66(6) & **92.08(1)** & 91.91(2) \\  & ImbVar\_Extreme\_SG & 89.44(4) & 85.23(6) & 89.52(3) & 82.88(7) & 70.89(8) & 88.90(5) & 91.82(2) & **92.51(1)** \\  & ImbVar\_Extreme\_SIG & 89.23(4) & 68.48(7) & 90.23(3) & 85.11(6) & 61.99(8) & 87.97(5) & 90.97(2) & **92.01(1)** \\ \hline \multirow{4}{*}{
\begin{tabular}{l} Real Stream \\ \end{tabular} } & PokerHand & 30.81(4) & 30.23(5) & 27.26(7) & 32.32(3) & 7.82(8) & 33.78(2) & 29.50(6) & **38.13(1)** \\  & Kddcup 99\_10\% & 35.19(6) & 28.29(7) & 40.02(3) & **44.80(1)** & 3.12(8) & 37.81(5) & 40.00(4) & 41.09(2) \\ \cline{1-1}  & Statlog(shuttle) & 44.13(7) & 45.81(5) & 50.12(4) & 44.45(6) & 17.61(8) & 52.41(3) & 56.73(2) & **78.41(1)** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Macro-Recall results (%) of the comparison experiments. As shown in Tables 5 and 6, HSDW-MI achieves the best macro-Recall and G-mean values for all synthetic and real data streams, ranking first, followed by the CALMID and ARF algorithms. For stationary, extremely imbalanced streams, HSDW-MI outperforms all other algorithms, with an average of 2.19% higher macro-Recall values and 3.13% higher G-mean values. In variable streams, HSDW-MI performs best overall, particularly excelling on ImbVar_Extreme_SG and ImbVar_Extreme_SIG with mixed drift, averaging 0.87% higher