TY - GEN
T1 - Optimal exact least squares rank minimization
AU - Xiang, Shuo
AU - Zhu, Yunzhang
AU - Shen, Xiaotong
AU - Ye, Jieping
PY - 2012
Y1 - 2012
N2 - In multivariate analysis, rank minimization emerges when a low-rank structure of matrices is desired as well as a small estimation error. Rank minimization is nonconvex and generally NP-hard, imposing one major challenge. In this paper, we consider a nonconvex least squares formulation, which seeks to minimize the least squares loss function with the rank constraint. Computationally, we develop efficient algorithms to compute a global solution as well as an entire regularization solution path. Theoretically, we show that our method reconstructs the oracle estimator exactly from noisy data. As a result, it recovers the true rank optimally against any method and leads to sharper parameter estimation over its counterpart. Finally, the utility of the proposed method is demonstrated by simulations and image reconstruction from noisy background.
AB - In multivariate analysis, rank minimization emerges when a low-rank structure of matrices is desired as well as a small estimation error. Rank minimization is nonconvex and generally NP-hard, imposing one major challenge. In this paper, we consider a nonconvex least squares formulation, which seeks to minimize the least squares loss function with the rank constraint. Computationally, we develop efficient algorithms to compute a global solution as well as an entire regularization solution path. Theoretically, we show that our method reconstructs the oracle estimator exactly from noisy data. As a result, it recovers the true rank optimally against any method and leads to sharper parameter estimation over its counterpart. Finally, the utility of the proposed method is demonstrated by simulations and image reconstruction from noisy background.
KW - global optimality
KW - nonconvex
KW - rank minimization
UR - http://www.scopus.com/inward/record.url?scp=84866045291&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84866045291&partnerID=8YFLogxK
U2 - 10.1145/2339530.2339609
DO - 10.1145/2339530.2339609
M3 - Conference contribution
AN - SCOPUS:84866045291
SN - 9781450314626
T3 - Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
SP - 480
EP - 488
BT - KDD'12 - 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
T2 - 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2012
Y2 - 12 August 2012 through 16 August 2012
ER -