TY - JOUR

T1 - A note on the correlated multiple matrix completion based on the convex optimization method

AU - Horii, Shunsuke

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeichi

PY - 2014

Y1 - 2014

N2 - In this paper, we consider a completion problem of multiple related matrices. Matrix completion problem is the problem to estimate unobserved elements of the matrix from observed elements. It has many applications such as collaborative filtering, computer vision, biology, and so on. In cases where we can obtain some related matrices, we can expect that their simultaneous completion has better performance than completing each matrix independently. Collective matrix factorization is a powerful approach to jointly factorize multiple matrices. However, existing completion algorithms for the collective matrix factorization have some drawbacks. One is that most existing algorithms are based on non-convex formulations of the problem. Another is that only a few existing algorithms consider the strength of the relation among matrices and it results in worse performance when some matrices are actually not related. In this paper, we formulate the multiple matrix completion problem as the convex optimization problem. Moreover, it considers the strength of the relation among matrices. We also develop an optimization algorithm which solves the proposed problem efficiently based on the alternating direction method of multipliers (ADMM). We verify the effectiveness of our approach through numerical experiments on both synthetic data and real data set: MovieLens.

AB - In this paper, we consider a completion problem of multiple related matrices. Matrix completion problem is the problem to estimate unobserved elements of the matrix from observed elements. It has many applications such as collaborative filtering, computer vision, biology, and so on. In cases where we can obtain some related matrices, we can expect that their simultaneous completion has better performance than completing each matrix independently. Collective matrix factorization is a powerful approach to jointly factorize multiple matrices. However, existing completion algorithms for the collective matrix factorization have some drawbacks. One is that most existing algorithms are based on non-convex formulations of the problem. Another is that only a few existing algorithms consider the strength of the relation among matrices and it results in worse performance when some matrices are actually not related. In this paper, we formulate the multiple matrix completion problem as the convex optimization problem. Moreover, it considers the strength of the relation among matrices. We also develop an optimization algorithm which solves the proposed problem efficiently based on the alternating direction method of multipliers (ADMM). We verify the effectiveness of our approach through numerical experiments on both synthetic data and real data set: MovieLens.

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U2 - 10.1109/smc.2014.6974147

DO - 10.1109/smc.2014.6974147

M3 - Conference article

AN - SCOPUS:84938154134

VL - 2014-January

SP - 1618

EP - 1623

JO - Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics

JF - Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics

SN - 1062-922X

IS - January

M1 - 6974147

T2 - 2014 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2014

Y2 - 5 October 2014 through 8 October 2014

ER -