Feature normalization for similarity calculations in matrix factorization method

Matrix factorization is a well-established approach in recommender systems with its roots in document retrieval. In this approach the original matrix of interactions between users and items is approximately factorized into matrices representing user features and item features. In this paper we argue for an orthogonality condition, under which the rows of the user feature matrix can be used to estimate similarity between users (and similarly for item similarity). Furthermore we provide an algebraic derivation of a normalization procedure to ensure that orthogonality conditions holds for any matrix factorization technique regardless of the rank of the factors. Finally we demonstrate the improvement in similarity ratings when the aforementioned normalization is applied to both explicit ratings and implicit feedback datasets, using the Alternating Least Square with Weighted λ-Regularization and Bayesian Probabilistic Matrix Factorization models.