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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationConference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1618-1623
Number of pages6
Volume2014-January
EditionJanuary
DOIs
Publication statusPublished - 2014
Event2014 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2014 - San Diego, United States
Duration: 2014 Oct 52014 Oct 8

Other

Other2014 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2014
CountryUnited States
CitySan Diego
Period14/10/514/10/8

Fingerprint

Convex optimization
Factorization
Collaborative filtering
Computer vision

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Human-Computer Interaction

Cite this

Horii, S., Matsushima, T., & Hirasawa, S. (2014). A note on the correlated multiple matrix completion based on the convex optimization method. In Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics (January ed., Vol. 2014-January, pp. 1618-1623). [6974147] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/smc.2014.6974147

A note on the correlated multiple matrix completion based on the convex optimization method. / Horii, Shunsuke; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. Vol. 2014-January January. ed. Institute of Electrical and Electronics Engineers Inc., 2014. p. 1618-1623 6974147.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Horii, S, Matsushima, T & Hirasawa, S 2014, A note on the correlated multiple matrix completion based on the convex optimization method. in Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. January edn, vol. 2014-January, 6974147, Institute of Electrical and Electronics Engineers Inc., pp. 1618-1623, 2014 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2014, San Diego, United States, 14/10/5. https://doi.org/10.1109/smc.2014.6974147
Horii S, Matsushima T, Hirasawa S. A note on the correlated multiple matrix completion based on the convex optimization method. In Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. January ed. Vol. 2014-January. Institute of Electrical and Electronics Engineers Inc. 2014. p. 1618-1623. 6974147 https://doi.org/10.1109/smc.2014.6974147
Horii, Shunsuke ; Matsushima, Toshiyasu ; Hirasawa, Shigeichi. / A note on the correlated multiple matrix completion based on the convex optimization method. Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. Vol. 2014-January January. ed. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 1618-1623
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