# Variational Autoencoders-Based Algorithm for Multi-Criteria Recommendation Systems
## 4 Experimental Results and Discussion
### Results and Discussion  
Table 6 provides a detailed evaluation of prediction accuracy using the VAE-MCRS model and other recommender systems on the Yahoo! dataset. The proposed VAE-MCRS model demonstrates the highest accuracy with an MAE of 0.6038 and an RMSE of 0.7085, showing its superiority to predict ratings accurately. The MCEDSL and MMEDSL methods show strong performance. These results indicate that both methods effectively utilize autoencoder-based frameworks for multi-criteria data, with the VAE demonstrating superiority over the traditional AE in learning from multi-criteria inputs. The ability of the VAE to capture complex latent representations and handle the variability inherent in multi-criteria ratings allows it to provide more accurate predictions. This good performance shows that the VAE can understand the relations between different criteria, which makes it helpful for collaborative filtering tasks where many factors affect what users like. We also compared our proposed model with SC-UCF, a single-criterion model, which performs less effectively with an MAE of 0.8720 and an RMSE of 0.9843, highlighting its limitations in capturing complex user preferences compared with multi-criteria methods. MC-UCF, which uses a multi-criteria CF approach, shows an MAE of 0.7722 and an RMSE of 0.8617, indicating better accuracy than SC-UCF but still not as satisfactory as the other advanced models. For MovieANN, which uses a multilayer feedforward neural network for multi-criteria ratings and has an MAE of 0.7190 and an RMSE of 0.7834, the performance is good but not like the precision of the VAE-MCRS model. For AEMC, utilizing a deep autoencoder-based approach achieves an MAE of 0.6435 and an RMSE of 0.7257, which is considered a very good result but does not perform as well as the VAE-MCRS model. In summary, the VAE-MCRS model excels in the integration of multi-criteria data with deep learning techniques, with the most accurate predictions compared with the other methods tested. The VAE-MCRS model presents several advantages alongside some limitations when compared with the techniques outlined in Table 6. One of its key strengths is its ability to capture complex, nonlinear patterns in user preferences, allowing for a nuanced representation of user-item interactions across multiple criteria. This model is particularly \begin{table}
\begin{tabular}{c c c} \hline \hline
**Approach** & **RMSE** & **MAE** \\ \hline SC-UCF [26] & 0.9843 & 0.8720 \\ \hline MC-UCF [6] & 0.8617 & 0.7722 \\ \hline MMEDSL [24] & 0.8133 & 0.6881 \\ \hline MovieANN [25] & 0.7834 & 0.7190 \\ \hline AEMC [21] & 0.7257 & 0.6435 \\ \hline MCEDSL [24] & 0.7202 & 0.6077 \\ \hline Proposed VAE-MCRS & **0.7085** & **0.6038** \\ \hline \hline \end{tabular} Bold values highlight the best performance.  
\end{table} 
Table 6: Prediction accuracy across all methods. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Optimizer**} & \multicolumn{3}{c}{**VAE-MCRS**} \\ \cline{2-3}  & **MAE** & **RMSE** \\ \hline Adagrad & 0.9236 & 1.2086 \\ \hline Adam & **0.6038** & **0.7085** \\ \hline RMSprop & 0.6795 & 0.8604 \\ \hline SGD & 1.3558 & 1.7642 \\ \hline \hline \end{tabular} Bold values highlight the best performance.  
\end{table} 
Table 5: Effect of the optimizer on the model performances. adept at handling data sparsity, as it learns a probability distribution over the latent space, making it effective in scenarios where users have rated only a small subset of items. Furthermore, VAE-MCRS utilizes a sequential training approach, uncovering relationships where preferences in one criterion may influence another, leading to a more comprehensive understanding of user behavior. Its generative capability also allows for the prediction of ratings for unrated items, effectively addressing the \"cold start\" problem. Experimental results indicate that VAE-MCRS outperforms baseline models in terms of accuracy, as evidenced by MAE and RMSE.