Instability of matrix factorization used in recommender systems

Abstract. The factorization of the matrices is not unique. The several different results of the factorization of a matrix would seem as reliable and consequently usable in the recommender systems if ones were stable. It means that the deducted conclusions are mainly the same without reference to differences in the product of the factor matrices. In this paper we discuss the interpretation of the stability of matrix factorization and give a few definitions. We ascertain that the matrix factorization is unstable.