Model selection for matrix factorization with missing components

The work is dedicated to the problem of factorizing a matrix with missing components into a product of two lower-rank matrices. The influence of the intensity of missing on the choice of the factorization model is studied. Two algorithms for parameter estimation are considered: alternating least squares (ALS) and Wiberg — for two factorization models: with and without means. It is substantiated that there is no need to use a model with averages: it is a special case of another model and, in some cases, leads to ambiguous solutions. During the experiments, the preference was given to a more stable ALS algorithm. The advantages of the insertion method over random filling in the initial settings of iterative algorithms for estimating model parameters are demonstrated. The reasons for the negative properties of the existing version of the Wiberg algorithm are revealed. Based on the experiments, it was found that with an increase in the probability of missing, the accuracy of the presentation of the available data increases which leads to an underestimation of the true value of the model dimension.