## 4 Experiments and Discussion
### Experimental Results and Discussion  
Experimental results in different datasets are shown in Tables 5-8, respectively. As a classical multi-label classification method, ML-KNN [40] distinguishes categories by measuring the distance between different feature values. This method is simple and insensitive to abnormal input. However, compared with ELM-based methods, the performance of ML-KNN [40] is always unsatisfactory, which also indicates the effectiveness of ELM. ML-ELM-RBF [41] improves the classification accuracy of ELM-RBF by stacking ELM-AE. Compared with ML-KNN [40], the performance of ML-ELM-RBF [41] is significantly improved, such as acquiring the best values of Hamming loss and one-error in computer dataset. To search the optimal solution, ML-KELM [42] employs a special projection framework and non-singular transformation matrix. Experimental results show that this method achieves competitive performance, especially obtaining the optimal values of Hamming loss and ranking loss in the art dataset. ML-CK-ELM [43] improves multi-label classification accuracy by optimizing the combination of multiple kernels; as a result, this approach is better than these previous methods in most indicators. Although without multi-layer staked structure, ELM-RBF-SAGA proposed in this paper is superior to ML-CK-ELM [43] on the whole, which fully demonstrates the effectiveness of SAGA in optimizing ELM-RBF. Table 9 lists the running time of different models in each dataset. It can be easily found from Table 9, as the representative of traditional machine learning methods, ML-KNN [40] is significantly slower than ELM-based models whether in the training or testing phase. In addition, this trend is especially evident with dataset's complexity increasing. Although our proposed method is not the fastest, it is faster than ML-CK-ELM [43] in art, computer, and yeast dataset. In summary, ELM-RBF-SAGA has obvious advantages over comparison methods and is very suitable for multi-label classification. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Evaluation Metric**} & \multicolumn{5}{c}{**Algorithm**} \\ \cline{2-6}  & **ML-KNN**[40] & **ML-ELM-RBF**[41] & **ML-KELM**[42] & **ML-CK-ELM**[43] & **ELM-RBF-SAGA** \\ \hline Average Precision & 0.5736 & 0.6078 & 0.6132 & 0.6263 & 0.6317 \\ Coverage & 4.7539 & 5.6723 & 5.2531 & 4.5864 & 4.5826 \\ Hamming Loss & 0.0576 & 0.0535 & 0.0531 & 0.0553 & 0.0533 \\ One-Error & 0.5132 & 0.4739 & 0.4732 & 0.4698 & 0.4683 \\ Ranking Loss & 0.1273 & 0.1387 & 0.1126 & 0.1143 & 0.1131 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance of different models in the yeast dataset. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Evaluation Metric**} & \multicolumn{5}{c}{**Algorithm**} \\ \cline{2-6}  & **ML-KNN**[40] & **ML-ELM-RBF**[41] & **ML-KELM**[42] & **ML-CK-ELM**[43] & **ELM-RBF-SAGA** \\ \hline Average Precision & 0.8826 & 0.8835 & 0.8863 & 0.8872 & 0.8886 \\ Coverage & 2.1576 & 2.5076 & 2.4964 & 2.4058 & 2.4032 \\ Hamming Loss & 0.0261 & 0.0258 & 0.0256 & 0.0232 & 0.0241 \\ One-Error & 0.1213 & 0.1163 & 0.1143 & 0.1156 & 0.1135 \\ Ranking Loss & 0.0356 & 0.0392 & 0.0369 & 0.0376 & 0.0342 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance of different models in the business dataset. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Evaluation Metric**} & \multicolumn{5}{c}{**Algorithm**} \\ \cline{2-6}  & **ML-KNN**[40] & **ML-ELM-RBF**[41] & **ML-KELM**[42] & **ML-CK-ELM**[43] & **ELM-RBF-SAGA** \\ \hline Average Precision & 0.8826 & 0.8835 & 0.8863 & 0.8872 & 0.8886 \\ Coverage & 2.1576 & 2.5076 & 2.4964 & 2.4058 & 2.4032 \\ Hamming Loss & 0.0261 & 0.0258 & 0.0256 & 0.0232 & 0.0241 \\ One-Error & 0.1213 & 0.1163 & 0.1143 & 0.1156 & 0.1135 \\ Ranking Loss & 0.0356 & 0.0392 & 0.0369 & 0.0376 & 0.0342 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance of different models in the computer dataset.