# Variational Autoencoders-Based Algorithm for Multi-Criteria Recommendation Systems
## 3 Proposed Variational Autoencoder Model  
As presented in Figure 2, the proposed VAE-MCRS model is built on two core concepts: first, the sequential training of the VAE model on different datasets, and second, utilizing the VAE model for prediction. As shown in Figure 2, the VAE architecture comprises three main components: encoder, latent, and decoder layers. The encoder begins with an input layer containing m neurons, representing the number of movies. It includes a hidden layer with a reduced number of neurons, with several configurations tested in the experiment section to determine the optimal structure for the model. The latent layers contain parameters for the mean (\(\mu\)), standard deviation (\(\sigma\)), and latent variable (\(z\)). The decoder mirrors the encoder structure in reverse. It starts with z as the input layer, followed by a hidden layer, and concludes with an output layer that has the same number of neurons as the encoder's input layer. The proposed VAE-based model VAE-MCRS is trained sequentially on multiple criteria datasets to enhance the model's ability to understand complex user preferences in a collaborative filtering recommendation system. The use of multiple criteria ratings like Acting,Story, Direction, and Visuals helps the model to capture the dependencies and correlations between these criteria, which leads to more personalized and accurate recommendations. The interaction between criteria is modeled by leveraging the latent feature space in the VAE. Specifically, after training on a criterion, the learned representations capture the unique patterns of that criteria. When the model moves to the next criterion, the previously learned latent features provide a foundation that enhances the model's ability to capture correlations between criteria, as these are inherently influenced by the patterns established in the earlier training stages. During training, each criterion-specific dataset is passed through the VAE, which consists of an encoder and a decoder. The encoder compresses the user-item interactions into a latent representation, while the decoder reconstructs these interactions, refining the latent features as it iterates through each criterion. This sequential training across multiple criteria progressively enhances the model's capability to learn complex interactions that might exist across different aspects of user preferences. As shown in Figure 2, the VAE-MCRS learning process begins with training the VAE model on the dataset for the first criterion. During this phase, the model parameters are optimized to identify the patterns between the first criterion ratings and the overall ratings, which serve as the output to be predicted by the model. Once the training with the first criterion dataset is complete, the model is then trained on the dataset for the next criterion. This process continues in sequence for each criterion dataset. The sequential aspect of the proposed approach enables the VAE-MCRS model to identify patterns where a user preference for one criterion might influence or correlate with another. For example, a user who prefers to always rate movies highly based on the visuals criteria might also prefer movies with strong direction criteria. By training the model with all criteria sequentially, it learns these multi-dimensional patterns, improving its ability to predict overall user preferences more effectively. In addition, training the same model sequentially on all criteria leads to more robust recommendations instead of training a distinct model for each criterion task. The model can predict a user overall movie rating by combining the criteria. This helps the model to generalize better across various types of movie ratings and provide recommendations that reflect user preferences. This approach can also better handle situations where users may not have provided ratings for all criteria.