## 4 Experimental Results
### Comparison between Visual Comfort Regression Model and the Mathematical Model  
The purpose of the real-world demonstration was to validate the performance of the pre-trained model as described in Section 3.3 in different rooms during the various seasons of the year, which are characterized by different daylight levels and daylight hours. For this reason, data from luminance sensors placed in two different rooms (the living room and double room) of CERTH's Smart Home [31] were retrieved over the course of a year.  
The \(w\) values were then calculated based on the date and time at which these luminance values were retrieved, as well as the coordinates of CERTH's Smart Home, in order to properly define the sunrise, sunset, and twilight times. Next, the \(w\) and \(lux\) values were fed into the pre-trained model to produce the estimated value of the \(VC\) in these particular conditions and time frames. The estimated \(VC\) values (i.e., regression model) were then compared with the actual \(VC\) values (i.e., mathematical model) calculated by solving Equation (1) with the same values of \(w\) and \(lux\). The results are presented in Table 7. It may be observed that the execution time improved by 95%. A 95% improvement in execution time from 0.19 s brings significant application benefits. It enables faster response times, improved efficiency, scalability for handling larger workloads, and enhanced user satisfaction. Additionally, it provides a competitive advantage for a model that needs to operate in real time.  
Furthermore, the results of this real-world experiment are presented in the figures below (Figures 9-20). In order to avoid an overwhelming number of figures, the results from the CERTH Smart Home living room are presented for the months of January, March, May, July, September, and November, while results from the double room are presented for the rest of the year. It should be noted that the visual assessment method utilizing decision tree regression (Figures 9-20) demonstrated exceptional results, with an impressively low average root mean squared error (RMSE) of 0.0056. This implied that the predicted values closely aligned with the ground truth values, indicating a high level of accuracy and precision in the model's predictions. The negligible RMSE value showcased the effectiveness of the regression technique in capturing and analyzing visual data, making it a reliable and trustworthy method for visual assessments.  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**Month**} & \multicolumn{2}{l}{**Mathematical Model Execution Time (sec)**} & \multicolumn{2}{l}{**Regression Model Execution Time (sec)**} & \multirow{2}{*}{**MSE**} & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{**R2**} \\ \cline{2-2} \cline{5-6}  & 0.19 & & & & 0.0034 & 0.0583 & 0.99 \\ \hline February & 0.19 & & 0.01 & & 0.0079 & 0.0889 & 0.99 \\ \hline March & 0.19 & & 0.01 & & 0.0112 & 0.1058 & 0.99 \\ \hline April & 0.19 & & 0.01 & & 0.0023 & 0.0480 & 0.99 \\ \hline May & 0.19 & & 0.01 & & 0.0002 & 0.0141 & 0.99 \\ \hline June & 0.19 & & 0.01 & & 0.0003 & 0.0173 & 0.99 \\ \hline July & 0.19 & & 0.01 & & 0.0009 & 0.0300 & 0.99 \\ \hline August & 0.19 & & 0.01 & & 0.0028 & 0.0529 & 0.99 \\ \hline September & 0.19 & & 0.01 & & 0.022 & 0.1483 & 0.99 \\ \hline October & 0.19 & & 0.01 & & 0.0017 & 0.0412 & 0.99 \\ \hline November & 0.19 & & 0.01 & & 0.0034 & 0.0583 & 0.99 \\ \hline December & 0.19 & & 0.01 & & 0.0115 & 0.1072 & 0.99 \\ \hline Average & & 0.19 & & 0.01 & & 0.0056 & 0.0642 & 0.99 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of regression algorithm and mathematical model results.  
Figure 11: March 2022.  
Figure 10: February 2022.  
Figure 9: January 2022.  
Figure 14: June 2022.  
Figure 12: April 2022.  
Figure 13: May 2022.  
Figure 16: August 2022.  
Figure 17: September 2022.  
Figure 15: July 2022.