Hastie, T., Mazumder, R., Lee, J.D. and Zadeh, R. (2015) Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares. Journal of Machine Learning Research, 16, 3367-3402.

has been cited by the following article:

• TITLE: The Equivalence between Orthogonal Iterations and Alternating Least Squares

  AUTHORS: Achiya Dax

  KEYWORDS: Alternating Least Squares (ALS), Orthogonal Iterations, Equivalence Relations, Low-Rank Approximations

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.10 No.2, April 30, 2020

  ABSTRACT: This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank-k approximation of a real m×n matrix, A. This method has important applications in nonnegative matrix factorizations, in matrix completion problems, and in tensor approximations. The second method is called Orthogonal Iterations. Other names of this method are Subspace Iterations, Simultaneous Iterations, and block-Power method. Given a real symmetric matrix, G, this method computes k dominant eigenvectors of G. To see the relation between these methods we assume that G = AT A. It is shown that in this case the two methods generate the same sequence of subspaces, and the same sequence of low-rank approximations. This equivalence provides new insight into the convergence properties of both methods.