Matrix Factorization for Movie Recommendations in Python

matrix-factorizationsvdrecommender-systemsmovielenspython

Abstraction: Low-rank SVD matrix factorization for collaborative filtering movie recommendations

Key points:

Decomposes user-movie ratings matrix R into U Σ V^T (SVD); U encodes user-feature affinity, V^T encodes movie-feature affinity
Low-rank approximation with k=50 latent factors; neighborhood methods overfit sparse raw data and fail to capture latent preferences
Limitation of neighborhood methods illustrated: two users with no overlapping RHCP songs get dot-product 0 despite similar taste
De-means ratings by user mean before factorization; uses scipy.sparse.linalg.svds to directly compute rank-k approximation
For movies, k between 20–100 generalizes best to unseen data; higher k overfits training ratings
Probabilistic matrix factorization and hybrid neighborhood+factorization models outperform pure SVD in production

Connections: Movielens · Matrix Factorization · Singular Value Decomposition · Collaborative Filtering · Recommender Systems