TY - GEN
T1 - An iterative algorithm for singular value decomposition on noisy incomplete matrices
AU - Cho, Kyunghyun
AU - Reyhani, Nima
PY - 2012
Y1 - 2012
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=84865074118&partnerID=8YFLogxK
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U2 - 10.1109/IJCNN.2012.6252789
DO - 10.1109/IJCNN.2012.6252789
M3 - Conference contribution
AN - SCOPUS:84865074118
SN - 9781467314909
T3 - Proceedings of the International Joint Conference on Neural Networks
BT - 2012 International Joint Conference on Neural Networks, IJCNN 2012
T2 - 2012 Annual International Joint Conference on Neural Networks, IJCNN 2012, Part of the 2012 IEEE World Congress on Computational Intelligence, WCCI 2012
Y2 - 10 June 2012 through 15 June 2012
ER -