Matrix Factorization
Matrix factorization is a powerful method to uncover latent relationships in large datasets. At its core, it breaks a large matrix into the product of two smaller ones, capturing the hidden structure of the data.
Case study: the Netflix Prize
When Netflix launched its famous competition to improve movie recommendations, matrix factorization emerged as the winning approach. Instead of treating user ratings as isolated points, it modeled both users and movies in a shared latent space. Each user was represented by a vector encoding their preferences (e.g., romance vs. action), and each movie by a vector encoding its attributes. The dot product of the two vectors predicted how much the user would enjoy the movie.
Why it works
- Dimensionality reduction: condenses massive data into a manageable form.
- Pattern discovery: reveals implicit associations (e.g., users who like “The Matrix” may also like “Blade Runner”).
- Scalability: works even when most of the matrix is missing (sparse data).
Practical uses
- Recommender systems (movies, music, shopping).
- Topic modeling in natural language processing.
- Bioinformatics, e.g., predicting protein interactions.
Limitations
Matrix factorization assumes that data can be explained by linear relationships. It may struggle with highly nonlinear or context-dependent behaviors. That’s why modern systems often combine it with deep learning architectures.
📖 References
- Koren, Y. et al. (2009). Matrix Factorization Techniques for Recommender Systems.
