Machine Learning Algorithms - Second Edition

Alternating least squares strategy

The problem of finding the latent factors can be easily expressed as a least squares optimization problem by defining the following loss function:

L is limited only to known samples (user, item). The second term works as a regularization factor, and the whole problem can easily be solved with any optimization method. However, there's an additional issue: we have two different sets of variables to determine (user and item factors). We can solve this problem with an approach called Alternating Least Squares (ALS), described in Matrix Factorization Techniques for Recommender Systems, Koren Y, Bell R, Volinsky ...