# English Speech Emotion Classification Based on Multi-Objective Differential Evolution
## 4 Experimental Results and Analysis
### Experimental Analysis  
#### 4.2.1 Simulation Results on the KNN Classifier  
1. Hypervolume (HV)  
Table 3 provides the HV of the algorithms where \(AVG\) and \(STD\) denote the average and variance of the HV, respectively. MODE-NSF outperformed MOGA, MODE, and NSGA-II using eNTERFACE05, RAVDESS, and SAVEE, while NSGA-II obtained the best HV value using TESS. The algorithms achieved low HV values using eNTERFACE05 and RAVDESS, but high values using TESS. The multi-objective algorithms performed poorly in the Pareto optimal solutions for the eNTERFACE05 and RAVDESS datasets, while the optimal solutions for TESS were close to the ideal value. The Wilcoxon rank sum revealed that MOGA, MODE, NSGA-II, and MODE-NSF performed well on 0, 0, 3, and 4 datasets. MODE-NSF and NSGA-II produced similar experimental data for RAVDESS, SAVEE, and TESS. According to the Friedman test, their average ranks were 3, 4, 1.75, and 1.25, respectively, proving that MODE-NSF performed the best, followed by NSGA-II, MOGA, and MODE. The NSF improves the multi-objective solution ability of DE. 2. Inverted generational distance (IGD)  
Table 4 shows the IGD of the algorithms, along with their Wilcoxon rank-sum and Friedman test results. MODE-NSF exhibited the best performance using eNTERFACE05, \begin{table}
\begin{tabular}{l l} \hline \hline
**Algorithm** & **Main Parameters** \\ \hline MOGA & PC = 1; mu = 0.02; \\ MODE & PCR = 0.2; \\ NSGA-II & tournament; mu = 20; mum = 20; \\ MODE-NSF & PCR = 0.2; beta\_min = 0.2; beta\_max = 0.8; \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameter settings of the algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**MOGA**} & \multicolumn{2}{c}{**MODE**} & \multicolumn{2}{c}{**NSGA-II**} & \multicolumn{2}{c}{**MODE-NSF**} \\ \cline{2-9}  & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline eNTERFACE05 & 0.0242 & 0.0364 & 0.0129 & 0.0278 & 0.0798 & 0.0578 & **0.1476** & 0.0842 \\ RAVDESS & 0.0408 & 0.0471 & 0.0195 & 0.0221 & 0.1343 & 0.0320 & **0.1356** & 0.0542 \\ SAVEE & 0.0915 & 0.0619 & 0.0538 & 0.0462 & 0.2140 & 0.0390 & **0.2334** & 0.0428 \\ TESS & 0.1640 & 0.1118 & 0.1078 & 0.0925 & **0.4545** & 0.1244 & 0.4254 & 0.1251 \\ \(>\)/\(=\)/\(<\) & 0/0/4 & & 0/0/4 & & 1/2/1 & & 3/1/0 \\ Rank & 3 & & 4 & & 1.75 & & 1.25 \\ \(p\)-Value & \(1.12\times\) & & & & & & \\  & \(10^{-2}\) & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The HV values of the algorithms. RAVDESS, SAVEE, and TESS. MODE-NSF's values were lower than those of the other algorithms, but its solutions were almost the same as the Pareto solutions obtained by them. The Wilicion rank sum indicates that MOGA, MODE, and NSGA-II did not share similar statistical data with MODE-NSF on the four datasets. The average ranks obtained by the Frideman test were 3, 4, 2, and 1, and the \(p\)-value was 1.12 \(\times\) 10\({}^{-2}\). Experimental data and non-parameter validation show that MODE-NSF outperformed MOGA, MODE, and NSGA-II in terms of IGD. The hypervolume, inverted generational distance, and non-parametric statistical analysis verified that MODE-NSF has a remarkable distribution and convergence, and it balances exploration and exploitation. 3. Pareto solutions  
Figure 3 shows the final Pareto optimal solutions acquired by the algorithms in which Pareto solutions were the solutions that were non-dominated and obtained from all algorithms after 20 runs.