Abstract

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend the orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix pursuit iteration and find satisfactory results in a few iterations. Another advantage of our proposed algorithm is that it has only one tunable parameter, which is the rank. It is easy to understand and to use by the user. This becomes especially important in large-scale learning problems. In addition, we rigorously show that both versions achieve a linear convergence rate, which is significantly better than the previous known results. We also empirically compare the proposed algorithms with several state-of-the-art matrix completion algorithms on many real-world datasets, including the large-scale recommendation dataset Netflix as well as the MovieLens datasets. Numerical results show that our proposed algorithm is more efficient than competing algorithms while achieving similar or better prediction performance.

Original languageEnglish (US)
Pages (from-to)A488-A514
JournalSIAM Journal on Scientific Computing
Volume37
Issue number1
DOIs
StatePublished - 2015

Fingerprint

Matrix Completion
Low-rank Matrices
Pursuit
Iteration
Matching Pursuit
Linear Convergence
Performance Prediction
Updating
Convergence Rate
Recommendations
Economics
Numerical Results

Keywords

  • Low rank
  • Matching pursuit
  • Matrix completion
  • Rank minimization
  • Singular value decomposition

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Orthogonal rank-one matrix pursuit for low rank matrix completion. / Wang, Zheng; Lai, Ming Jun; Lu, Zhaosong; Fan, Wei; Davulcu, Hasan; Ye, Jieping.

In: SIAM Journal on Scientific Computing, Vol. 37, No. 1, 2015, p. A488-A514.

Research output: Contribution to journalArticle

Wang, Zheng ; Lai, Ming Jun ; Lu, Zhaosong ; Fan, Wei ; Davulcu, Hasan ; Ye, Jieping. / Orthogonal rank-one matrix pursuit for low rank matrix completion. In: SIAM Journal on Scientific Computing. 2015 ; Vol. 37, No. 1. pp. A488-A514.
@article{bf7696e769284a5093d1476cc8d08108,
title = "Orthogonal rank-one matrix pursuit for low rank matrix completion",
abstract = "In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend the orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix pursuit iteration and find satisfactory results in a few iterations. Another advantage of our proposed algorithm is that it has only one tunable parameter, which is the rank. It is easy to understand and to use by the user. This becomes especially important in large-scale learning problems. In addition, we rigorously show that both versions achieve a linear convergence rate, which is significantly better than the previous known results. We also empirically compare the proposed algorithms with several state-of-the-art matrix completion algorithms on many real-world datasets, including the large-scale recommendation dataset Netflix as well as the MovieLens datasets. Numerical results show that our proposed algorithm is more efficient than competing algorithms while achieving similar or better prediction performance.",
keywords = "Low rank, Matching pursuit, Matrix completion, Rank minimization, Singular value decomposition",
author = "Zheng Wang and Lai, {Ming Jun} and Zhaosong Lu and Wei Fan and Hasan Davulcu and Jieping Ye",
year = "2015",
doi = "10.1137/130934271",
language = "English (US)",
volume = "37",
pages = "A488--A514",
journal = "SIAM Journal of Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

TY - JOUR

T1 - Orthogonal rank-one matrix pursuit for low rank matrix completion

AU - Wang, Zheng

AU - Lai, Ming Jun

AU - Lu, Zhaosong

AU - Fan, Wei

AU - Davulcu, Hasan

AU - Ye, Jieping

PY - 2015

Y1 - 2015

N2 - In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend the orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix pursuit iteration and find satisfactory results in a few iterations. Another advantage of our proposed algorithm is that it has only one tunable parameter, which is the rank. It is easy to understand and to use by the user. This becomes especially important in large-scale learning problems. In addition, we rigorously show that both versions achieve a linear convergence rate, which is significantly better than the previous known results. We also empirically compare the proposed algorithms with several state-of-the-art matrix completion algorithms on many real-world datasets, including the large-scale recommendation dataset Netflix as well as the MovieLens datasets. Numerical results show that our proposed algorithm is more efficient than competing algorithms while achieving similar or better prediction performance.

AB - In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend the orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix pursuit iteration and find satisfactory results in a few iterations. Another advantage of our proposed algorithm is that it has only one tunable parameter, which is the rank. It is easy to understand and to use by the user. This becomes especially important in large-scale learning problems. In addition, we rigorously show that both versions achieve a linear convergence rate, which is significantly better than the previous known results. We also empirically compare the proposed algorithms with several state-of-the-art matrix completion algorithms on many real-world datasets, including the large-scale recommendation dataset Netflix as well as the MovieLens datasets. Numerical results show that our proposed algorithm is more efficient than competing algorithms while achieving similar or better prediction performance.

KW - Low rank

KW - Matching pursuit

KW - Matrix completion

KW - Rank minimization

KW - Singular value decomposition

UR - http://www.scopus.com/inward/record.url?scp=84923857523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923857523&partnerID=8YFLogxK

U2 - 10.1137/130934271

DO - 10.1137/130934271

M3 - Article

VL - 37

SP - A488-A514

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 1

ER -