# Variational Autoencoders-Based Algorithm for Multi-Criteria Recommendation Systems
## 4 Experimental Results and Discussion
### Sensitivity Analysis  
Multiple assessments were performed to identify the best values for the VAE-MCRS model hyperparameters, such as the number of hidden layers, optimization algorithms, and activation functions.  
Table 1 displays the hyperparameter values tested in the experiments to find the optimal settings for the proposed model. Table 2 illustrates the optimal hyperparameters of the VAE-MCRS model.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameters** & **Experiments Using** \\ \hline Optimizer & Adagrad, SGD, Adam, RMSprop \\ \hline Activation Functions & Softmax, ELU, RELU, Sigmoid \\ \hline Hidden Layers & \(7,5,3\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Hyperparameters of the VAE-MCRS model.  
Figure 3: Yahoo dataset sample.  
Table 3 demonstrates the impact of different values of the number of hidden layers on VAE-MCRS's effectiveness. The findings show that three hidden layers provide the most optimal performance for VAE-MCRS. Increasing the number of hidden layers leads to higher MAE and RMSE, indicating potential overfitting with deeper architectures.  
The results of the sensitivity analysis in Table 4 highlight the impact of various activation functions on the VAE-MCRS model effectiveness. Combining the ELU activation function in the hidden layers and the Sigmoid function in the output layer yields the best performance, with an MAE of 0.6038 and an RMSE of 0.7085. In contrast, using ELU in both layers results in higher errors, while the ELU-Softmax combination improves performance but does not surpass the ELU-Sigmoid configuration. The results demonstrate that the Sigmoid activation function is most effective for mapping discrete ratings to the discrete range of [1; 5].  
Table 5 summarizes the results obtained by applying VAE-MCRS with four different optimizers. The analysis reveals that the VAE-MCRS model achieved its best performance using the Adam optimizer, while the RMSprop optimizer provided the optimal results for the VAE-MCRS model with the highest performance metrics.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Activation Function**} & \multicolumn{2}{c}{**VAE-MCRS**} \\ \hline
**Hidden Layers** & **Output Layer** & **MAE** & **RMSE** \\ \hline ELU & ELU & 0.7231 & 1.054 \\ \hline ELU & Softmax & 0.6709 & 0.7903 \\ \hline ELU & Sigmoid & **0.6038** & **0.7085** \\ \hline RELU & Sigmoid & 0.6102 & 0.7125 \\ \hline \hline \end{tabular} Bold values highlight the best performance.  
\end{table}
Table 4: Effect of activation functions on the model performances.  
\begin{table}
\begin{tabular}{l c} \hline \hline \multicolumn{2}{c}{**Hyperparameters**} & **VAE-MCRS** \\ \hline Output Layer Activation Function & Sigmoid \\ \hline Hidden Layers Activation Function & ELU \\ \hline Number of Hidden Layers & 3 \\ \hline Optimizer & Adam \\ \hline dropout & 0.5 \\ \hline Learning Rate & 0.01 \\ \hline Epochs with Early Stopping & 100 \\ \hline Batch Size & 32 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Tuned hyperparameters of VAE-MCRS.  
\begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{2}{c}{**Hidden Layers**} & \multicolumn{2}{c}{**VAE-MCRS**} \\ \cline{2-3}  & **MAE** & **RMSE** \\ \hline
**3 Layers** & **0.6038** & **0.7085** \\ \hline
**5 Layers** & 0.6691 & 0.8099 \\ \hline
**7 Layers** & 0.7016 & 0.8849 \\ \hline \hline \end{tabular} Bold values highlight the best performance.  
\end{table}
Table 3: Effect of hidden layer on the model performances.