Matrix Factorization and Hybrid Recommender Systems
Explore how matrix factorization addresses data sparsity in recommender systems by learning latent user and item factors. Understand alternating least squares for factor estimation, scoring with implicit feedback, and blending collaborative with content-based scores to enhance recommendations. Learn to handle cold-start issues and balance collaborative and content signals for better personalized suggestions.
When most entries in a user-item matrix are empty, item-to-item similarity can rest on only one or two shared interactions. Those similarities become noisy, so a neighborhood recommender may rank an unrelated course highly or have no useful neighbors at all. Matrix factorization addresses that sparsity by learning a compact representation for each user and each item.
A latent factor is a learned numeric dimension that summarizes a hidden preference pattern without carrying a fixed label. One factor might behave like interest in advanced compliance material, while another might behave like preference for technical subjects. The model learns several numbers for a user and several numbers for a course. Their dot product produces a plausible preference score for a user-course pair that has no recorded interaction.
Instead of comparing each course directly with every other course, factorization compresses the interaction matrix into smaller user and item factor matrices. The compression can reveal shared patterns even when two users never interacted with the same exact course.
Reconstructing a ratings matrix
A small explicit-rating matrix makes the compression visible. Here, NaN means that a learner did not rate a movie, while ratings from 1 through 5 are observed preferences. The code fills missing ratings with 0 only so TruncatedSVD can run in this compact demonstration. A real recommender must distinguish an unknown interaction from a true zero-valued signal.
The reconstruction follows this relationship:
Here,