# Box Constrained Low-rank Matrix Approximation with Missing Values

### Manami Tatsukawa, Mirai Tanaka

#### Abstract

In this paper, we propose a new low-rank matrix approximation model for completing a matrix with missing values. Our proposed model contains a box constraint that arises from the context of collaborative filtering. Although it is unfortunately NP-hard to solve our model with high accuracy, we can construct a practical algorithm to obtain a stationary point. Our proposed algorithm is based on alternating minimization and converges to a stationary point under a mild assumption.

Download#### Paper Citation

#### in Harvard Style

Tatsukawa M. and Tanaka M. (2018). **Box Constrained Low-rank Matrix Approximation with Missing Values**.In *Proceedings of the 7th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-285-1, pages 78-84. DOI: 10.5220/0006612100780084

#### in Bibtex Style

@conference{icores18,

author={Manami Tatsukawa and Mirai Tanaka},

title={Box Constrained Low-rank Matrix Approximation with Missing Values},

booktitle={Proceedings of the 7th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2018},

pages={78-84},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006612100780084},

isbn={978-989-758-285-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 7th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Box Constrained Low-rank Matrix Approximation with Missing Values

SN - 978-989-758-285-1

AU - Tatsukawa M.

AU - Tanaka M.

PY - 2018

SP - 78

EP - 84

DO - 10.5220/0006612100780084