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Bounded matrix low rank approximation

Boekbijdrage - Hoofdstuk

Low rank approximation is the problem of finding two matrices P∈Rm×k and Q∈Rk×n for input matrix R∈Rm×n, such that R≈PQ. It is common in recommender systems rating matrix, where the input matrix R is bounded in the closed interval [rmin,rmax] such as [1, 5]. In this chapter, we propose a new improved scalable low rank approximation algorithm for such bounded matrices called bounded matrix low rank approximation (BMA) that bounds every element of the approximation PQ. We also present an alternate formulation to bound existing recommender systems algorithms called BALS and discuss its convergence. Our experiments on real-world datasets illustrate that the proposed method BMA outperforms the state-of-the-art algorithms for recommender system such as stochastic gradient descent, alternating least squares with regularization, SVD++ and bias-SVD on real-world datasets such as Jester, Movielens, Book crossing, Online dating, and Netflix.
Boek: Non-negative Matrix Factorization Techniques
Pagina's: 89-118
Aantal pagina's: 30
Jaar van publicatie:2016
Trefwoorden:Signal, Image and Speech Processing, Computer Imaging, Vision, Pattern Recognition and Graphics, Computational Mathematics and Numerical Analysis, Artificial Intelligence (incl. Robotics), Biomedical Engineering