## 6 Example Validation
### Parameter Setting  
The relevant parameters of the autoencoder when carrying out Experiment 1 and Experiment 7 are shown in Table 3 below. The batch size is set as the sample size of the dataset due to the small sample size of the dataset for the experimental design.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Encoding Method**} & \multirow{2}{*}{**Code Dimension**} & \multicolumn{6}{c}{**Total Input Dimensions**} \\ \cline{3-8}  & & & **Piping** & **Hull Structure** & **Gait** & **Restaurant** & **Fish** & **Abbreviation** \\ \hline \multirow{3}{*}{1} & Orthogonal matrix-autoencoder-based encoding method & \multirow{3}{*}{1} & \multirow{3}{*}{8} & \multirow{3}{*}{4} & \multirow{3}{*}{6} & \multirow{3}{*}{7} & \multirow{3}{*}{6} & \multirow{3}{*}{O-AE} \\ \cline{1-1} \cline{5-8}  & Embedding & & & & & & & \\ \cline{1-1} \cline{5-8}  & & & & & & & & \\ \cline{1-1} \cline{5-8}  & & Number of & & & & & & \\ \cline{1-1} \cline{5-8}  & & categories (N) & & & & & & \\ \hline \multirow{2}{*}{5} & Label encoding & \multirow{2}{*}{1} & \multirow{2}{*}{8} & \multirow{2}{*}{4} & \multirow{2}{*}{6} & \multirow{2}{*}{7} & \multirow{2}{*}{6} & \multirow{2}{*}{LE} \\ \cline{1-1} \cline{5-8}  & & & & & & & & \\ \hline \multirow{3}{*}{7} & \multirow{3}{*}{The hyperparameters of the autoencoder for O-AE} & \multirow{3}{*}{1} & \multirow{3}{*}{8} & \multirow{3}{*}{4} & \multirow{3}{*}{6} & \multirow{3}{*}{7} & \multirow{3}{*}{6} & \multirow{3}{*}{O-AE-b} \\ \cline{1-1} \cline{5-8}  & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: The experimental design and the total input dimensions after encoding.  
In particular, in Experiment 7, the unordered multi-categorical variables are divided into training and validation sets according to 7:3. The early-stopping strategy is introduced, and the patience parameter for early stopping is set to 100. The number of AE hidden layers and the number of nodes per layer are obtained with Bayesian optimization. The number of encoder hidden layers is set to be no more than five, and the decoder and encoder structures are symmetric.  
The number of hidden layers of the autoencoder and the number of nodes in each layer in Experiment 1 are manually and dynamically adjusted according to different datasets. The epoch of Experiment 1 was kept the same as Experiment 7. Also, since there is no additional autoencoder hyperparameter optimization procedure for Experiment 1 and in order to compare with other experiments to demonstrate the applicability of Experiment 1, the early-stopping strategy is not used.  
To carry out target prediction using a BP neural network, the dataset is divided into a training set, validation set, and test set in the ratio of 7:2:1.  
The relevant parameters are shown in Table 4. The batch size is set as the sample size of the dataset due to the small sample size of the dataset for the experimental design. In order to quickly conduct experiments and obtain a better prediction result, the hyperparameter optimization method of a 5-fold cross-validation grid search is used, and the number of nodes in each hidden layer is set to be the same; the number of optional hidden layers and the number of optional nodes are shown in Table 4. In order to improve the model performance and avoid overfitting, we introduce L2 Regularization and early-stopping strategy and set the patience parameter of early stopping to 100.  
Meanwhile, the original code generation step randomly generates \(N\)-order square matrix \(\mathbf{A}\in\mathbb{R}^{N\times N}\) based on the number of categories \(N\) in the unordered multi-categorical variables and fixes the random seed to ensure that the experimental data are the same.