A Mathematical Optimization Approach for Preference Learning in Movie Recommender Systems with Shared Accounts

A recommender system typically assumes that each row of the user-item rating matrix reflects the preferences of a single user. However, in many cases, an account is shared among multiple household members, resulting in mixed ratings data that do not accurately represent individual preferences. As a consequence, the recommendations will fail to align with the specific interests of each user. To address this issue, we introduce the concept of a “user character,” which represents a common latent factor in both movie and account features. By establishing a movie feature matrix based on these character representations, we can identify the presence of different characters in shared accounts. This is achieved by factoring the account feature binary matrix from the rating matrix, a process that can be modeled as a binary quadratic optimization problem. For scalability, we relax the binary constraint using a penalty function and approximate the solutions through the gradient descent method. Additionally, we apply a thresholding function to obtain binary solutions that reveal the user characters within each account. Once we identify the characters associated with each account, we can learn users' distinct preferences through a demixing procedure. This allows us to reconstruct the rating matrix so that each row accurately represents a single user's preferences. To evaluate our method, we generated a shared account dataset from MovieLens ratings based on the CAMRa2011 dataset. Experiments conducted on this dataset demonstrate the effectiveness of our proposed approach.