## 6 Example Validation
### Target Prediction Results  
Under the above parameter settings, several calculations are carried out to obtain the results of the evaluation metrics for the five datasets in seven experiments. The number of nodes per layer of the encoding layer of the autoencoder (the decoding layer is symmetrical to the structure of the encoding layer, so the description is omitted) and the number of layers and nodes in the hidden layer of the BP neural network after hyperparameter optimization are shown in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Loss Function** & **Activation Function** & **Optimizer** & **Learning Rate** & **Epoch** \\ \hline MSE & Relu & Adam & 0.001 & \(1000\) \\ \hline
**L2 Regularization** & **Batch size** & **Patience** & **Optional hidden layers** & **Optional nodes** \\ \hline
0.0001 & Sample size (\(\widetilde{N}\)) & 100 & \(10,20,30\) & \(1,2,3\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The parameter setting of the BP neural network. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Experiment** & \begin{tabular}{c} **Loss** \\ **Function** \\ \end{tabular} & \
\begin{tabular}{c} **Activation** \\ **Function** \\ \end{tabular} & **Optimizer** &
\begin{tabular}{c} **Learning** \\ **Rate** \\ \end{tabular} & **Epoch** & **Batch Size** & **Patience** \\ \hline O-AE & MSE & Relu & Adam & 0.001 & 2000 & Sample size (\(\widetilde{N}\)) & - \\ \hline O-AE-b & MSE & Relu & Adam & 0.001 & 2000 & Sample size (\(\widetilde{N}\)) & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameter setting of the autoencoder in O-AE and O-AE-b. In this paper, we denote the model structure of the autoencoder by unordered multi-categorical variables' original dimension \(-\) intermediate compression dimension \(-\) 1. The results of the evaluation metrics for the five datasets in seven experiments are shown in Table 6.  
This paper plots the results of the target prediction experiments for each dataset, including the fitted regression plots between the predicted and actual values in the test set, as shown in Figures 4-8, and the line charts between the predicted and actual values in the test set, as shown in Figures 9-13. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **O-AE** & **1-EE** & **5-EE** & **OHE** & **LE** & **TE** & **O-AE-b** \\ \hline \multirow{3}{*}{Piping} & MAE & **4.3681** & 6.8860 & 6.1809 & 4.8380 & 5.6480 & **8.1285** & 4.5841 \\  & RMSE & 5.8296 & 9.8875 & 9.9672 & 7.9449 & 9.2587 & **11.1007** & **5.7244** \\  & \(R^{2}\) & 0.9718 & 0.9189 & 0.9175 & 0.9476 & 0.9288 & **0.8977** & **0.9728** \\ \hline \multirow{3}{*}{Hull structure} & MAE & 8.4987 & 12.3219 & 10.6569 & 6.4534 & 9.9077 & **14.3765** & **5.8390** \\  & RMSE & 10.2222 & 17.5980 & 15.5944 & 12.5951 & 15.5421 & **19.2587** & **7.6556** \\  & \(R^{2}\) & 0.9628 & 0.8896 & 0.9133 & 0.9435 & 0.9139 & **0.8678** & **0.9791** \\ \hline \multirow{3}{*}{Gait} & MAE & 3.4295 & 3.4297 & 3.1289 & 3.6434 & 3.8893 & **4.2187** & **3.3678** \\  & RMSE & 4.5314 & 4.7570 & 4.6198 & 5.1868 & 5.1943 & **5.7029** & **4.2098** \\  & \(R^{2}\) & 0.9319 & 0.9250 & 0.9292 & 0.9108 & 0.9105 & **0.8921** & **0.9412** \\ \hline \multirow{3}{*}{Restaurant} & MAE & **40.8338** & **42.3132** & 42.3016 & 41.4832 & 41.1913 & 41.6640 & 40.9350 \\  & RMSE & 52.6461 & 54.2528 & 53.0498 & 52.8340 & 53.3646 & 52.6894 & **51.9348** \\ \cline{1-1}  & \(R^{2}\) & 0.7559 & **0.7407** & 0.7521 & 0.7541 & 0.7492 & 0.7555 & **0.7624** \\ \hline \multirow{3}{*}{Fish} & MAE & 21.7449 & 24.5180 & 22.9351 & **20.7503** & 23.8476 & **56.8344** & 20.8339 \\ \cline{1-1}  & RMSE & 32.1668 & 34.4302 & 34.8801 & 33.4807 & 33.7599 & **72.4618** & **31.8064** \\ \cline{1-1}  & \(R^{2}\) & 0.9867 & 0.9848 & 0.9844 & 0.9856 & 0.9854 & **0.9327** & **0.9870** \\ \hline \hline \end{tabular} Bold indicates the best and worst values of the evaluation metrics.  
\end{table} 
Table 6: The results of the evaluation metrics.