Scalable algorithms for locally low-rank matrix modeling

Qilong Gu, Joshua D Trazasko, Arindam Banerjee

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

Abstract

We consider the problem of modeling data matrices with locally low rank (LLR) structure, a generalization of the popular low rank structure widely used in a variety of real world application domains ranging from medical imaging to recommendation systems. While LLR modeling has been found to be promising in real world application domains, limited progress has been made on the design of scalable algorithms for such structures. In this paper, we consider a convex relaxation of LLR structure, and propose an efficient algorithm based on dual projected gradient descent (D-PGD) for computing the proximal operator. While the original problem is non-smooth, so that primal (sub)gradient algorithms will be slow, we show that the proposed D-PGD algorithm has geometrical convergence rate. We present several practical ways to further speed up the computations, including acceleration and approximate SVD computations. With experiments on both synthetic and real data from MRI (magnetic resonance imaging) denoising, we illustrate the superior performance of the proposed D-PGD algorithm compared to several baselines.

Original languageEnglish (US)
Title of host publicationProceedings - 17th IEEE International Conference on Data Mining, ICDM 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages137-146
Number of pages10
Volume2017-November
ISBN (Electronic)9781538638347
DOIs
StatePublished - Dec 15 2017
Event17th IEEE International Conference on Data Mining, ICDM 2017 - New Orleans, United States
Duration: Nov 18 2017Nov 21 2017

Other

Other17th IEEE International Conference on Data Mining, ICDM 2017
CountryUnited States
CityNew Orleans
Period11/18/1711/21/17

Fingerprint

Recommender systems
Medical imaging
Magnetic resonance
Singular value decomposition
Data structures
Imaging techniques
Experiments

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Gu, Q., Trazasko, J. D., & Banerjee, A. (2017). Scalable algorithms for locally low-rank matrix modeling. In Proceedings - 17th IEEE International Conference on Data Mining, ICDM 2017 (Vol. 2017-November, pp. 137-146). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICDM.2017.23

Scalable algorithms for locally low-rank matrix modeling. / Gu, Qilong; Trazasko, Joshua D; Banerjee, Arindam.

Proceedings - 17th IEEE International Conference on Data Mining, ICDM 2017. Vol. 2017-November Institute of Electrical and Electronics Engineers Inc., 2017. p. 137-146.

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

Gu, Q, Trazasko, JD & Banerjee, A 2017, Scalable algorithms for locally low-rank matrix modeling. in Proceedings - 17th IEEE International Conference on Data Mining, ICDM 2017. vol. 2017-November, Institute of Electrical and Electronics Engineers Inc., pp. 137-146, 17th IEEE International Conference on Data Mining, ICDM 2017, New Orleans, United States, 11/18/17. https://doi.org/10.1109/ICDM.2017.23
Gu Q, Trazasko JD, Banerjee A. Scalable algorithms for locally low-rank matrix modeling. In Proceedings - 17th IEEE International Conference on Data Mining, ICDM 2017. Vol. 2017-November. Institute of Electrical and Electronics Engineers Inc. 2017. p. 137-146 https://doi.org/10.1109/ICDM.2017.23
Gu, Qilong ; Trazasko, Joshua D ; Banerjee, Arindam. / Scalable algorithms for locally low-rank matrix modeling. Proceedings - 17th IEEE International Conference on Data Mining, ICDM 2017. Vol. 2017-November Institute of Electrical and Electronics Engineers Inc., 2017. pp. 137-146
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