## 3 Result Analysis
### Results of Thermal Models with Classification Algorithms
However, for the feature set A, SVM still achieves high precision, recall and f1 scores which indicates that SVM can be the best classifier with the feature set consisting of indoor air temperature, relative humidity, skin temperature and clothing surface temperature for both the female and male subject. Therefore, such a combination is recommended to be the thermal model for real-time prediction for automatic personalized heating and cooling system in open-plan offices. Moreover, Figures 7 and 8 show the normalized confusion matrices on test data with the three feature sets for the two subjects by using SVM and RF, respectively. The normalization equation is shown below:  
\[x_{norm\_ij}=\frac{x_{ij}}{\sum_{k=1}^{k=m}x_{ik}} \tag{7}\]  
where \(x_{norm\_ij}\) is the normalized value of cell \(x_{ij}\), which is the element in the \(i\)th row and \(j\)th column. In addition, \(m\) is the number of the column of the confusion matrix. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Base Feature Set**} & \multicolumn{3}{c}{**Feature Set A**} & \multicolumn{3}{c}{**Feature Set B**} \\ \cline{2-10}  & **P (\%)** & **R (\%)** & **F1 (\%)** & **P (\%)** & **R (\%)** & **F1 (\%)** & **P (\%)** & **R (\%)** & **F1 (\%)** \\ \hline SVM & 62.3 & 62.9 & 62 & 100 & 100 & 100 & 69.2 & 64.7 & 65.1 \\ RF & 57.7 & 48.6 & 48.6 & 91.6 & 91.4 & 91 & 49 & 47 & 46.3 \\ PMV & 48.6 & 48.6 & 48.3 & 48.6 & 48.6 & 48.3 & 48.6 & 48.6 & 48.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance benchmark among the thermal models of the female subject. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Base Feature Set**} & \multicolumn{3}{c}{**Feature Set A**} & \multicolumn{3}{c}{**Feature Set B**} \\ \cline{2-10}  & **P (\%)** & **R (\%)** & **F1 (\%)** & **P (\%)** & **R (\%)** & **F1 (\%)** & **P (\%)** & **R (\%)** & **F1 (\%)** \\ \hline SVM & 33.5 & 42.5 & 35.8 & **97.5** & **95** & **96.1** & 32.1 & 43.6 & 34.5 \\ RF & 28.8 & 40 & 33.1 & 90.4 & 9 As to the female subject, the test data with neutral label has the highest accuracy for each feature set. With both SVM and RF, for base feature set, the test data with cold (\(-2\)) label has the lowest accuracy  
Figure 8: Normalized confusion matrix of the male subject. (**a**) Base Feature set with SVM, (**b**) Feature set A with SVM, (**c**) Feature set B with SVM, (**d**) Base Feature set with RF, (**e**) Feature set A with RF, (**f**) Feature set B with RF. Figure 7: Normalized confusion matrix of the female subject. (**a**) Base Feature set with SVM, (**b**) Feature set A with SVM, (**c**) Feature set B with SVM, (**d**) Base Feature set with RF, (**e**) Feature set A with RF, (**f**) Feature set B with RF. while for feature set B, the test data with cool (-1) label has the lowest accuracy. As to male subject, same as female subject, the test data with neutral label has the highest accuracy for each feature set. Moreover, as shown in Table 5, the number of uncomfortable sensations is much smaller than that of neutral sensation. Therefore, it is more difficult to predict uncomfortable thermal sensations, including cold/hot (-2/2) and very cold/very hot (-3/3) than neutral sensation. However, as shown in the figures, SVM performs better in predicting uncomfortable thermal sensations than RF for both subjects.