Matrix factorization has been used heavily in recommendation systems, text-mining, spectral data analysis. his post is just about keeping all the resources about matrix factorization that I have found. Just remember that the code listing here might not directly fulfill your requirements. If you have a sparse matrix then make sure weather the programs assume missing entries as zero or as unknowns, this will affect your result very drastically. Also, make sure that you have at least one element in each row and each column. Some theoretical results suggest that an order of (n log n) entries might be required to successfully recover the unknown matrix (These entries are very lose at the moment). Make sure you have enough data.

**Applications**

- Matrix Factorization Techniques for Recommender Systems: An article by Koren, Bell and Volinsky in IEEE computer magazine.

**Algorithms and Code**

- Netflix Update: Try this at Home: This is such a nice online resource that it has been cited by many research papers.
- Matrix Factorization: A Simple Tutorial and Implementation in Python: This page explains all the math around a stochastic descent for matrix factorization.
- Timely Development: Some Analysis of the Netflix data with C++ code.

**Large Scale Implementation**

- Large-Scale Matrix Factorization with Distributed Stochastic Gradient Descent:
*KDD 2011*paper by R Gemulla*et. al.* - Distributed Nonnegative Matrix Factorization for Web-Scale Dyadic Data Analysis on MapReduce:
*WWW 2010*paper by C Liu*et. al.*