# Noise-Tolerant Data Reconstruction Based on Convolutional Autoencoder for Wireless Sensor Network +
## 5 Experiment and Evaluation
### Performance Evaluation
#### 5.2.2 Performance Comparison  
We conducted an experiment using the PM 2.5 dataset to verify the effectiveness of the SCAE model. Particularly, both internal and external noise affect sensed data simultaneously. Training and testing errors are the two performance metrics used to evaluate the efficiency of the proposed framework. Table 5 summarizes the simulation results when running the experiments with the process dataset using several existing reconstruction techniques. We selected partial least squares regression (PLSR) [35] and a bidirectional recurrent neural network (RNN) [18] because they are popular and traditional regression techniques that can be used for reconstruction. As shown in Table 5, the proposed stacked CNN achieved the best results with a training error of 1.06% and a testing error of 1.09%. In addition to investigating the performance of the proposed framework using the parameters provided in Table 2, we conducted experiments involving varying degrees of severity for different types of weather situations. A survey of weather conditions at different levels using the PM 2.5 dataset is carried out in Table 6. It can be seen that weather conditions have a significant impact on the performance of data reconstruction after using the proposed SCAE model. As weather conditions worsen, the ability of data reconstruction to function effectively decreases. This is due to the increased attenuation of signals between the sensor receiver and the transmitter. Essentially, when the weather is severe, more of the transmitted data are lost, making it more challenging to recover the information. In addition, experiments were conducted to investigate the influence of internal noise on the performance of data reconstruction using the PM 2.5 dataset. The noise variance value is determined within the range of 0.1 to 1, with no consideration of weather-related factors. Figures 8 and 9 provide convincing evidence of the enhanced performance shown by the proposed approach in comparison with the original CAE. In particular, with a variance of noise of 0.1, the training error of the SCAE is 1.33, whereas that of the CAE is 2.54. When the variance of the noise was raised to a value of 1, the training error of the CAE exhibited a rise of more than twice the magnitude compared with that of the SCAE. Similarly, the test error gap between the SCAE and CAE is 1.38 when \(\delta^{2}_{\text{noise}}=0.1\); however, it increases to 2.73 when \(\delta^{2}_{\text{noise}}=1\). It is obvious that the SCAE consistently outperforms the CAE with varying noise variance. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Number of Dense Layers** & **0** & **1** & **3** & **5** & **7** \\ \hline Training Error (\%) & 2.12 & 1.92 & 1.52 & 1.06 & 1.42 \\ Testing Error (\%) & 2.23 & 2.21 & 1.65 & 1.09 & 1.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of results when using the SCAE model with different numbers of dense layers. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Algorithm** & **Training Errors \%** & **Testing Errors \%** \\ \hline Partial Least Squares Regression & 3.37 & 3.42 \\ Bidirectional RNN & 2.57 & 2.69 \\ CAE & 1.53 & 1.55 \\
**SCAE** & **1.06** & **1.09** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance comparisons among existing reconstruction algorithms using the PM 2.5 dataset. In addition to the PM 2.5 dataset that we used to evaluate the efficiency of the proposed SCAE network, we also conducted experiments with many different datasets, such as the temperature, air quality index (AQI), O3, and PM 10 listed in Table 7. It can be observed that the SCAE operates efficiently with different datasets and outperforms the normal CAE. Therefore, it can be concluded that using stack techniques for pretraining the weights significantly improves the data reconstruction performance. The proposed model can discover a better local optimum than traditional AE models.