A rank minimization heuristic with application to minimum order system approximation

By Maryam Fazel, Haitham A. Hindi, Stephen P. Boyd. Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), 2001

1,090 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6503fcffc6692b99f467815d2a3471116115f5bd

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Citations in the corpus

Deterministic algorithms for matrix completion (2014, background): “More recently, the trace-norm and γ2 were suggested as alternative measures of complexity [5, 16].”
Sparse Modeling for Image and Vision Processing (2014, background): “Another form of parsimony has been devised in the spectral domain [Fazel et al., 2001, Srebro et al., 2005].”
Multitask learning meets tensor factorization: task imputation via convex optimization (2014, background): “where ∥ · ∥tr is the trace norm (also known as the nuclear norm) [10, 20], which is defined as the absolute sum of singular values.”
Optimization with Sparsity-Inducing Penalties (2011, background): “Using the trace norm as a convex surrogate for rank has many applications in control theory [48], matrix completion [1, 130], multi-task learning [109], or multi-label classification [4], where low-rank priors are adapted.”
Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices (2003, methodology): “This reduces to applying a weighted trace heuristic iteratively, and thus is related to the trace heuristic discussed in [ FHB01 ]: the rst iteration is the same as the usual trace minimization, and the next iterations tend to reduce the rank of the solution further.”
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations (2011, background): “…by the task of recovering the low-rank and sparse components of a given matrix (usually the matrix represents data obtained by observation), e.g. the model selection in statistics, matrix rigidity in computer science, system identification in engineering, [19] [20] [21] [38] [44] [46] [53].”
Consistency of trace norm minimization (2007, background): “First, we have the following result: Lemma 19 (Dual norm, Fazel et al., 2001) The trace norm k · ∗ is a norm and its dual norm is the operator norm k · k .”
Spectral k-Support Norm Regularization (2014, background): “We end this section by briefly discussing the cluster norm, which was introduced in [9] as a convex relaxation of a multitask clustering problem.”
Structured sparsity through convex optimization (2011, background): “nuclear norm) = sum of singular values • Convex function, leads to a semi-definite program (Fazel et al., 2001) • First used for collaborative filtering (Srebro et al.”
Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization (2014, background): “Recently, the low-rank and sparse matrix separation problem has attracted increasing research interest with potential applications in various areas such as statistics and system identiﬁcations [17, 18, 34].”
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization (2007, background): “, [1]), to a loworder controller for a plant (see, e.”
Nuclear Norm Based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes (2014, background): “Fazel et al. [18, 19] found that the convex envelope of rank (X) is the nuclear norm of X, i.e.”