Final answer:
Using a user's latent factor vector from the compressed SVD user matrix U_k and predicting ratings by multiplying with the movie matrix V_k, we can recommend the top n movies for that user. Therefore, the correct options are c) and d).
Step-by-step explanation:
The question pertains to the field of recommender systems, likely within a computer science or machine learning context. To recommend the top n movies to a user using compressed SVD (Singular Value Decomposition), we utilize the user's latent factors represented in the user matrix Uk and the movie's latent factors in the movie matrix Vk. The process is as follows:
- Identify the given user's latent factor vector from the user matrix Uk.
- Compute the predicted ratings by multiplying this vector by the movie matrix Vk.
- Sort these predicted ratings in descending order and select the top n movies as the recommendations.
To clarify the terms mentioned in the question:
- Singular Value:These are the diagonal elements of the matrix Sigma in the SVD and represent the strength of each latent factor.
- Singular Vector: The singular vectors form the columns of matrices U (left-singular vectors) and V (right-singular vectors) and represent the direction of latent factors in the user and movie space respectively.
- User Matrix (Uk): This is a reduced representation of original user preferences data, capturing the main 'k' latent factors affecting their preferences.
- Movie Matrix (Vk): This is a reduced representation of original movie attribute data, capturing the main 'k' latent factors that describe them.
Therefore, the correct options are c) and d).