Matrix Decomposition for Preference Prediction with Auxiliary Attributes

The patent introduces auxiliary information (user attributes, object attributes, context information) as intermediary elements that mediate between partial preference values and preference predictions. These auxiliary informations serve as bridges to infer missing preferences by finding similarities and patterns, thereby improving prediction accuracy without requiring complete preference data from all users.

The patent creates virtual copies of preference information by generating predicted preference values for user-object pairs where preferences are missing. Through matrix decomposition and factorization, the system reconstructs the preference matrix by copying patterns from observed preferences to unobserved ones, enabling comprehensive recommendations even with partial input data.

The patent extracts the essential structure of user preferences by decomposing the large preference matrix into smaller factor matrices representing user latent factors and object latent factors. This extraction process separates the complex many-to-many user-object preference relationships into simpler, lower-dimensional representations, reducing system complexity while preserving prediction accuracy.

The patent transforms the preference prediction problem by changing parameters from direct user-object preference values to latent factor representations. By projecting preferences into a lower-dimensional latent space and performing matrix factorization, the system reduces the complexity of handling large numbers of users and objects while maintaining the ability to make accurate predictions through dot product computations in the transformed space.