# Variational Autoencoders-Based Algorithm for Multi-Criteria Recommendation Systems
## 3 Proposed Variational Autoencoder Model
The VAE can learn how different criteria influence each other and combine them into one preference profile that reflects the complex dynamics of user preferences. * In a real case, users do not provide ratings for all criteria (for example, a user may rate Acting and Visuals, but omit Story and Direction). The VAE model, well regarded for handling missing data, addresses this challenge by inferring missing ratings based on the ratings provided. By learning the distribution of preferences across all users and criteria, the VAE can estimate likely values for unrated criteria. For instance, if a user rates highly on Acting and Direction but leaves Visuals unrated, the VAE can predict the likely Visuals rating based on patterns learned from similar users. This ability is crucial when training the model on multiple criteria datasets sequentially, as it ensures robust performance even when full information is not available for every user or criterion. * The VAE applies Gaussian distribution to the latent space for regularization. This regularization helps prevent overfitting to specific criteria and encourages the model to generalize across the dataset. As a result, the VAE balances the influence of each criterion and achieves a balanced representation of user preferences across all criteria (i.e., no single criterion dominates). * By training on all criteria datasets sequentially, the VAE can generate personalized recommendations that reflect users' true preferences across different aspects. Rather than optimizing the model for each criterion independently (which may lead to partial or less coherent recommendations), the VAE enables the model to understand how user ratings for criteria such as Acting, Story, Direction, and Visuals are correlated. For example, if a user rates Visuals'very good' but has moderate preferences for Acting, the VAE will use the learned latent representation to recommend movies that balance these preferences, like movies with strong visuals but average acting. It also enables the model to make a list of recommendations by understanding user preferences across different combinations of criteria. * When VAE is trained on a multi-criteria dataset, it can suggest items based on different aspects. For example, if a user favors Story and Visuals, the VAE might recommend a movie that excels in these aspects or suggest a movie with strong Direction and Acting, providing diverse relevant options. The proposed VAE-MCRS model is well suited for deployment across various real-world recommendation systems, making it practically relevant in industries such as e-commerce, streaming platforms, and tourism. Its flexible architecture allows for simple adaptation to specific domains by adjusting criteria to reflect domain-specific aspects. For example, in e-commerce, criteria could include product quality, price, brand, and customer reviews, enabling the model to deliver recommendations that more accurately match user preferences. The model can be integrated as a backend recommendation engine, processing user interactions and historical data to generate recommendations in real time. This adaptability and ease of integration demonstrate the model's utility for businesses looking to offer tailored, data-driven recommendations to their users.