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On the rank minimization problem

by Yoonsoo Kim, Mehran Mesbahi - In: Proceedings of the 2004 American Control Conference , 2004
"... Abstract — After a brief overview of the problem of finding the extremal (minimum or maximum) rank positive semidef-inite matrix subject to matrix inequalities, we identify a few new classes of such problems that can be efficiently solved. We then proceed to present an algorithm for solving the gene ..."
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the general class of rank minimization problems. Index Terms — Rank minimization under LMI constraints, semidefinite programming, nonconvex quadratically con-strained quadratic programs I.

Improved thresholds for rank minimizations

by Samet Oymak, M. Amin Khajehnejad, Babak Hassibi - in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP , 2011
"... Abstract—Nuclear norm minimization (NNM) has recently gained attention for its use in rank minimization problems. In this paper, we define weak, sectional and strong recovery for NNM to succeed at finding the low rank solution. We find tight conditions for these and analyze them for the case where t ..."
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Abstract—Nuclear norm minimization (NNM) has recently gained attention for its use in rank minimization problems. In this paper, we define weak, sectional and strong recovery for NNM to succeed at finding the low rank solution. We find tight conditions for these and analyze them for the case where

A Rank Minimization Heuristic with Application to Minimum Order System Approximation

by Maryam Fazel, Haitham Hindi, Stephen P. Boyd , 2001
"... Several problems arising in control system analysis and design, such as reduced order controller synthe-sis, involve minimizing the rank of a matrix vari-able subject to linear matrix inequality (LMI) con-straints. Except in some special cases, solving this rank minimization probiem (globally) is ve ..."
Abstract - Cited by 274 (10 self) - Add to MetaCart
Several problems arising in control system analysis and design, such as reduced order controller synthe-sis, involve minimizing the rank of a matrix vari-able subject to linear matrix inequality (LMI) con-straints. Except in some special cases, solving this rank minimization probiem (globally

Rank minimization and applications in system theory

by M. Fazel, H. Hindi, S. Boyd - In American Control Conference , 2004
"... Abstract-In this tutorial paper, we consider the problem Of minimizing the rank of a matrix over a convex set. The Rank Minimization Problem (RMP) arises in diverse areas such as control, system identification, statistics and signal processing, and is known to be computationally NP-hard. We give an ..."
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Abstract-In this tutorial paper, we consider the problem Of minimizing the rank of a matrix over a convex set. The Rank Minimization Problem (RMP) arises in diverse areas such as control, system identification, statistics and signal processing, and is known to be computationally NP-hard. We give

Improved Thresholds for Rank Minimization

by Babak Hassibi, Samet Oymak, M. Amin Khajehnejad, Babak Hassibi , 2011
"... All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.

Penalty decomposition methods for rank minimization

by Zhaosong Lu, Yong Zhang , 2010
"... In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first show that a class of matrix optimization problems can be solved as lower dimensional vector optimization problems. As a consequence, we establish that a class of rank ..."
Abstract - Cited by 8 (6 self) - Add to MetaCart
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first show that a class of matrix optimization problems can be solved as lower dimensional vector optimization problems. As a consequence, we establish that a class

Rank Minimization via Online Learning

by Raghu Meka, Prateek Jain, Constantine Caramanis, Inderjit S. Dhillon
"... Minimum rank problems arise frequently in machine learning applications and are notoriously difficult to solve due to the non-convex nature of the rank objective. In this paper, we present the first online learning approach for the problem of rank minimization of matrices over polyhedral sets. In pa ..."
Abstract - Cited by 16 (2 self) - Add to MetaCart
Minimum rank problems arise frequently in machine learning applications and are notoriously difficult to solve due to the non-convex nature of the rank objective. In this paper, we present the first online learning approach for the problem of rank minimization of matrices over polyhedral sets

Robust Late Fusion With Rank Minimization

by Guangnan Ye, Dong Liu, I-hong Jhuo, Shih-fu Chang
"... In this paper, we propose a rank minimization method to fuse the predicted confidence scores of multiple models, each of which is obtained based on a certain kind of feature. Specifically, we convert each confidence score vector obtained from one model into a pairwise relationship matrix, in which e ..."
Abstract - Cited by 14 (2 self) - Add to MetaCart
In this paper, we propose a rank minimization method to fuse the predicted confidence scores of multiple models, each of which is obtained based on a certain kind of feature. Specifically, we convert each confidence score vector obtained from one model into a pairwise relationship matrix, in which

Efficient Structured Matrix Rank Minimization

by Adams Wei Yu, et al.
"... We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use the full SVD; nor (b) resort to augmented Lagrangian techni ..."
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We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use the full SVD; nor (b) resort to augmented Lagrangian

Subspace Expanders and Matrix Rank Minimization

by Amin Khajehnejad, Samet Oymak, Babak Hassibi , 2013
"... Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that satisfies a set of linear constraints. The existing algorithms ..."
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Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that satisfies a set of linear constraints. The existing
Results 1 - 10 of 3,056