Bounded matrix low rank approximation

Ramakrishnan Kannan; Mariya Ishteva; Barry Drake; Haesun Park

doi:10.1007/978-3-662-48331-2_4

Bounded matrix low rank approximation

Ramakrishnan Kannan, Mariya Ishteva, Barry Drake, Haesun Park

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

4 Scopus citations

Abstract

Lowrank approximation is the problem of finding twomatrices P ∈ R^m×k and Q ∈ R^k×n for input matrix R ∈ R^m×n, such that R ≈ PQ. It is common in recommender systems rating matrix, where the input matrix R is bounded in the closed interval [r_min, r_max] 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 stateof-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.

Original language	English
Title of host publication	Non-negative Matrix Factorization Techniques
Subtitle of host publication	Advances in Theory and Applications
Publisher	Springer Berlin Heidelberg
Pages	89-118
Number of pages	30
ISBN (Electronic)	9783662483312
ISBN (Print)	9783662483305
DOIs	https://doi.org/10.1007/978-3-662-48331-2_4
State	Published - Sep 25 2015
Externally published	Yes

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AU - Drake, Barry

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AB - Lowrank approximation is the problem of finding twomatrices 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 stateof-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.

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Bounded matrix low rank approximation

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