# Improving Multi-Instance Multi-Label Learning by Extreme Learning Machine
## 4 Performance Evaluation
### Statistical Significance of the Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{C}\downarrow\) & **Image** & **Text** & **Geob.** & **Azoto.** & **average rank** \\ \hline SVM & 2.4712(4) & 2.235(4) & 2.439(4) & 2.317(4) & 4 \\ SVM + k & 1.9257(2) & 1.66(2) & 1.5833(2) & 1.6391(3) & 2.25 \\ ELM + k & 2.1451(3) & 1.7198(3) & 1.6247(3) & 1.6285(2) & 2.75 \\ ELM + k + w & 1.741(1) & 1.0928(1) & 1.372(1) & 1.361(1) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Friedman test of the gradual effectiveness evaluation on criterion \(C\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(i\) & **Classifier** & \(z=(R_{i}-R_{0})/SE\) & \(p\) & \(\alpha/(k-i)\) \\ \hline
1 & SVM & \((4-1)/0.913\approx 3.286\) & 0.0014 & 0.017 \\
2 & ELM + k & \((2.75-1)/0.913\approx 1.917\) & 0.0562 & 0.025 \\
3 & SVM + k & \((2.25-1)/0.913\approx 1.369\) & 0.1706 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: [PERSON] test of the gradual effectiveness evaluation on criterion \(C\). the adjusted \(\alpha\)'s. Thus, it is statically believed that MIMLELM with \(HN=200\) has a significant performance improvement of training over two of the MIMLSVM+ classifiers. In summary, the proposed framework can significantly improve the effectiveness of MIML learning. Equipped with the framework, the effectiveness of MIMLELM is comparable to that of MIMLSVM+, while the efficiency of MIMLELM is significantly better than that of MIMLSVM+. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Training Time\(\downarrow\)**} & **Image** & **Text** & **Geob.** & **Azoto.** & **average rank** \\ \hline \multirow{4}{*}{MIMLSVM+} & \(Cost=10^{-3},\gamma=2^{1}\) & 717.6202(10) & 284.75(10) & 46.582(8) & 50.3727(4) & 8 \\  & \(Cost=10^{-2},\gamma=2^{2}\) & 690.1484(4) & 283.86(7) & 46.41(6) & 50.6691(6) & 5.75 \\  & \(Cost=10^{-1},\gamma=2^{3}\) & 690.2365(5) & 284.02(8) & 46.27(5) & 50.9343(8) & 6.5 \\  & \(Cost=1,\gamma=2^{1}\) & 706.2458(6) & 283.65(6) & 46.8(9) & 51.0591(10) & 7.75 \\  & \(Cost=10^{1},\gamma=2^{3}\) & 710.6634(7) & 283.21(4) & 46.036(4) & 50.7315(7) & 5.5 \\  & \(Cost=10^{2},\gamma=2^{5}\) & 717.3216(8) & 283.59(5) & 46.4272(7) & 50.9344(9) & 7.25 \\  & \(Cost=10^{3},\gamma=2^{5}\) & 711.5548(9) & 284.47(9) & 46.8312(10) & 50.5936(5) & 8.25 \\ \hline \multirow{4}{*}{MIMLELM} & \(HN=100\) & 641.3661(1) & 210.55(2) & 38.657(2) & 41.4495(1) & 1.5 \\  & \(HN=200\) & 642.1002(2) & 211.29(3) & 38.922(3) & 41.9643(3) & 2.75 \\ \cline{1-1}  & \(HN=300\) & 644.2047(3) & 209.84(1) & 38.641(1) & 41.9019(2) & 1.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Friedman test of the training time. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**\(\mathbf{C\downarrow}\)**} & **Image** & **Text** & **Geob.** & **Azoto.** & **average rank** \\ \hline \multirow{4}{*}{MIMLSVM+} & \(Cost=10^{-3},\gamma=2^{1}\) & 1.2100(3) & 1.0295(4) & 1.5122(10) & 1.3171(5) & 5.5 \\  & \(Cost=10^{-2},\gamma=2^{2}\) & 1.1201(1) & 1.0405(6) & 1.2439(6) & 1.0732(3) & 4 \\  & \(Cost=10^{-1},\gamma=2^{3}\) & 1.1262(2) & 1.0445(7) & 1.0488(1) & 1.1707(4) & 3.5 \\  & \(Cost=1,\gamma=2^{1}\) & 1.9808(7) & 1.0145(2) & 1.0732(2) & 1.0488(5) & 3.25 \\  & \(Cost=10^{1},\gamma=2^{3}\) & 1.9999(8) & 1.0041(1) & 1.1707(4) & 1.0244(5) & 5.5 \\  & \(Cost=10^{2},\gamma=2^{5}\) & 1.9799(6) & 1.0450(8) & 1.1219(3) & 1.9512(9) & 6.5 \\  & \(Cost=10^{3},\gamma=2^{5}\) & 2.0000(9.5) & 1.0245(3) & 1.2195(5) & 1.9756(10) & 6.875 \\ \hline \multirow{4}{*}{MIMLELM} & \(HN=100\) & 2.0000(9.5) & 1.0670(9) & 1.3902(8) & 1.4732(8) & 8.625 \\  & \(HN=200\) & 1.7410(5) & 1.0928(10) & 1.3720(7) & 1.3610(6) & 7 \\ \cline{1-1}  & \(HN=300\) & 1.5700(4) & 1.0365(5) & 1.4025(9) & 1.4585(7) & 6.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Friedman test of the effectiveness comparison in Tables 2–5 on criterion \(C\).