Alternating Least-Squares (ALS) Matrix Factorization Algorithm

References

https://www.quora.com/What-is-the-Alternating-Least-Squares-method-in-recommendation-systems
- QUOTE: Alternating Least Squares (ALS) represents a different approach to optimizing the loss function. The key insight is that you can turn the non-convex optimization problem in Equation (2) into an "easy" quadratic problem if you fix either p_u or q_i. ALS fixes each one of those alternatively. When one is fixed, the other one is computed, and vice versa.
  There are two main benefits of this approach. First, this is very easy to parallelize. Second, whenever dealing with implicit datasets, which are usually not sparse, SGD is not practical (users times items can easily be in the order of billions). ALS is a much more efficient optimization technique in these cases.
  There are two main benefits of this approach. First, this is very easy to parallelize. Second, whenever dealing with implicit datasets, which are usually not sparse, SGD is not practical (users times items can easily be in the order of billions). ALS is a much more efficient optimization technique in these cases.

(Takács & Tikk, 2012) ⇒ Gábor Takács, and Domonkos Tikk. (2012). “Alternating Least Squares for Personalized Ranking.” In: Proceedings of the Sixth ACM Conference on Recommender System.