## 4 Experiments
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **PT-Bayes** & **PT-SVM** & **AA-BP** & **AA-kNN** & **FFRS-w** \\ \hline
1 & 6.382 \(\pm\) 0.305 & 0.921 \(\pm\) 0.107 & 2.352 \(\pm\) 0.173 & 0.758 \(\pm\) 0.040 & **0.685 \(\pm\) 0.047** \\
2 & 4.987 \(\pm\) 0.222 & 0.785 \(\pm\) 0.084 & 1.718 \(\pm\) 0.110 & 0.717 \(\pm\) 0.041 & **0.649 \(\pm\) 0.042** \\
3 & 4.461 \(\pm\) 0.282 & 0.691 \(\pm\) 0.047 & 1.488 \(\pm\) 0.098 & 0.644 \(\pm\) 0.016 & **0.587 \(\pm\) 0.019** \\
4 & 1.744 \(\pm\) 0.071 & 0.528 \(\pm\) 0.031 & 0.568 \(\pm\) 0.033 & 0.455 \(\pm\) 0.011 & **0.439 \(\pm\) 0.020** \\
5 & 1.415 \(\pm\) 0.102 & 0.396 \(\pm\) 0.016 & 0.459 \(\pm\) 0.031 & 0.392 \(\pm\) 0.010 & **0.371 \(\pm\) 0.008** \\
6 & 1.473 \(\pm\) 0.069 & 0.565 \(\pm\) 0.049 & 0.599 \(\pm\) 0.043 & 0.559 \(\pm\) 0.024 & **0.515 \(\pm\) 0.033** \\
7 & 0.845 \(\pm\) 0.059 & 0.267 \(\pm\) 0.014 & 0.268 \(\pm\) 0.015 & 0.260 \(\pm\) 0.013 & **0.243 \(\pm\) 0.009** \\
8 & 0.846 \(\pm\) 0.051 & 0.186 \(\pm\) 0.008 & 0.204 \(\pm\) 0.012 & 0.182 \(\pm\) 0.007 & **0.172 \(\pm\) 0.006** \\
9 & 0.681 \(\pm\) 0.038 & 0.287 \(\pm\) 0.019 & 0.291 \(\pm\) 0.018 & 0.297 \(\pm\) 0.016 & **0.285 \(\pm\) 0.019** \\
10 & 0.424 \(\pm\) 0.038 & 0.187 \(\pm\) 0.011 & 0.184 \(\pm\) 0.011 & 0.191 \(\pm\) 0.008 & **0.183 \(\pm\) 0.010** \\
11 & 3.24 \(\pm\) 3.634 & 14.63 \(\pm\) 0.647 & 22.79 \(\pm\) 1.841 & 16.28 \(\pm\) 0.818 & **14.51 \(\pm\) 0.650** \\
12 & 7.149 \(\pm\) 0.109 & 7.208 \(\pm\) 0.205 & 6.767 \(\pm\) 0.095 & **3.044 \(\pm\) 0.137** & 6.663 \(\pm\) 0.113 \\
13 & 0.904 \(\pm\) 0.086 & 0.935 \(\pm\) 0.074 & 1.046 \(\pm\) 0.124 & **0.843 \(\pm\) 0.113** & 0.889 \(\pm\) 0.085 \\
14 & 1.116 \(\pm\) 0.020 & 1.147 \(\pm\) 0.064 & 1.051 \(\pm\) 0.064 & **0.841 \(\pm\) 0.014** & 0.900 \(\pm\) 0.041 \\
15 & 1.547 \(\pm\) 0.075 & 1.537 \(\pm\) 0.216 & 1.269 \(\pm\) 0.089 & 1.276 \(\pm\) 0.046 & **1.120 \(\pm\) 0.050** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results (mean \(\pm\) std (rank)) of the Clark distance (the smaller the better). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No. ** & **PT-Bayes** & **PT-SVM** & **AA-BP** & **AA-kNN** & **FFRS-w** \\ \hline
1 & 0.743 \(\pm\) 0.015 & 0.991 \(\pm\) 0.002 & 0.949 \(\pm\) 0.006 & 0.994 \(\pm\) 0.001 & **0.995 \(\pm\) 0.001** \\
2 & 0.766 \(\pm\) 0.017 & 0.991 \(\pm\) 0.002 & 0.960 \(\pm\) 0.004 & 0.992 \(\pm\) 0.001 exhibited better performance than AA-kNN in most datasets. The average ranks of these algorithms are shown in Figure 7, where FRFS-w always ranks at the top among all four measurements. AA-kNN maintained the structure information of the labels. However, PT-SVM destroyed the distribution structure during the process of transforming the data, and therefore, PT-SVM exhibited results that were worse than AA-kNN. PT-Bayes exhibited good performances when the data matched the Gaussian assumption required by the algorithm. However, its performance fell when operated on other real datasets. Too many parameters in AA-BP led to poor performance because it is difficult to find the optimized settings. The FFRS-w algorithm learns more information from the data. The lower and upper approximations are the measures of necessity and possibility. They are combined to form the interval, of which the weights of each label are trained and used to evaluate the test data. This process improves the robustness of the algorithm. Therefore, FFRS-w exhibits better performances than AA-kNN.