An iterative algorithm for singular value decomposition on noisy incomplete matrices

Kyunghyun Cho, Nima Reyhani

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

Abstract

In this paper, we propose a simple iterative algorithm, called iSVD, for estimating the singular value decomposition (SVD) of a noisy incomplete given matrix. The iSVD relies on first order optimization over orthogonal manifolds and automatically estimates the rank of the SVD. The main goal here is to estimate the singular vectors through optimization in the right space, which is the space of the orthogonal matrix manifolds. The rank estimation is based on the ratio between estimated large singular values and the sum of all singular values. We empirically evaluate the iSVD on synthetic matrices and image reconstruction tasks. The evaluation shows that the iSVD is comparable to the recently introduced methods for matrix completion such as singular value thresholding (SVT) and fixed-point iteration with approximate SVD (FPCA).

Original languageEnglish (US)
Title of host publication2012 International Joint Conference on Neural Networks, IJCNN 2012
DOIs
StatePublished - 2012
Event2012 Annual International Joint Conference on Neural Networks, IJCNN 2012, Part of the 2012 IEEE World Congress on Computational Intelligence, WCCI 2012 - Brisbane, QLD, Australia
Duration: Jun 10 2012Jun 15 2012

Other

Other2012 Annual International Joint Conference on Neural Networks, IJCNN 2012, Part of the 2012 IEEE World Congress on Computational Intelligence, WCCI 2012
CountryAustralia
CityBrisbane, QLD
Period6/10/126/15/12

Fingerprint

Singular value decomposition
Image reconstruction

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence

Cite this

Cho, K., & Reyhani, N. (2012). An iterative algorithm for singular value decomposition on noisy incomplete matrices. In 2012 International Joint Conference on Neural Networks, IJCNN 2012 [6252789] https://doi.org/10.1109/IJCNN.2012.6252789

An iterative algorithm for singular value decomposition on noisy incomplete matrices. / Cho, Kyunghyun; Reyhani, Nima.

2012 International Joint Conference on Neural Networks, IJCNN 2012. 2012. 6252789.

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

Cho, K & Reyhani, N 2012, An iterative algorithm for singular value decomposition on noisy incomplete matrices. in 2012 International Joint Conference on Neural Networks, IJCNN 2012., 6252789, 2012 Annual International Joint Conference on Neural Networks, IJCNN 2012, Part of the 2012 IEEE World Congress on Computational Intelligence, WCCI 2012, Brisbane, QLD, Australia, 6/10/12. https://doi.org/10.1109/IJCNN.2012.6252789
Cho K, Reyhani N. An iterative algorithm for singular value decomposition on noisy incomplete matrices. In 2012 International Joint Conference on Neural Networks, IJCNN 2012. 2012. 6252789 https://doi.org/10.1109/IJCNN.2012.6252789
Cho, Kyunghyun ; Reyhani, Nima. / An iterative algorithm for singular value decomposition on noisy incomplete matrices. 2012 International Joint Conference on Neural Networks, IJCNN 2012. 2012.
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