Matrix Factorization

Matrix factorization decomposes a user-item interaction matrix into lower-dimensional latent factor matrices.

$$R\approx P{Q}^T$$

Where:

• $R$ is the user-item rating matrix
• $P$ is the user latent factor matrix
• $Q$ is the item latent factor matrix
• $k$ is the number of latent factors

Intuition

Users and items are represented in the same latent space. A user’s preference for an item is estimated by the dot product between the user’s vector and the item’s vector.

Common Algorithms

• SVD
• Also (Alternating Least Squares)
• NMF (Non-negative Matrix Factorization)

Role In Recommendation

Matrix factorization is useful when direct interactions are sparse but there are enough patterns to infer latent preferences. It is a model-based form of Collaborative Filtering.

Limitations

Matrix factorization can struggle with new users or new items because they do not yet have reliable interaction vectors. This is one reason Hybrid Recommendation System combines collaborative and content-based features.