Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices

By Maryam Fazel, Haitham A. Hindi, Stephen P. Boyd. Proceedings of the 2003 American Control Conference, 2003., 2003

654 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/575124bd6f7fda9f33f0aef2c707395eeb5121bf

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Citations in the corpus

Robust principal component analysis? (2009, background): “This was suggested for rank minimization in [16, 45] and for low-rank and sparse decomposition [12] (see also [35]).”
Hankel Matrix Rank Minimization with Applications to System Identification and Realization (2013, neutral): “where the optimization variable is y ∈ R2N−1 with yi corresponding to the value of the impulse response at time i, li and bi denoting the bounds on the step response given by the specifications, and H(y) denoting an N ×N Hankel matrix; see [18] for more details.”
Iterative reweighted algorithms for matrix rank minimization (2012, methodology): “The Reweighted ℓ 1 algorithm has also been generalized to the recovery of low-rank matrices (Fazel et al., 2003; Mohan and Fazel, 2010a).”
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization (2007, background): “y= Ah, where h= [h(0);:::;h(N)]0, and A ij= a i(N j). From linear system theory, the order of the minimal realization for such a system is given by the rank of the following Hankel matrix (see, e.g., [29, 46]) hank(h) := 2 6 6 6 4 h(0) h(1) h(N) h(1) h(2) h(N+ 1) .. . .. . .. . h(N) h(N+ 1) h(2N) 3 ”
A New View of Automatic Relevance Determination (2007, methodology): “A related optimization strategy has also been reported in [3].”
Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization (2014, background): “Recently, the low-rank and sparse matrix separation (SMS) problem has attracted increasing research interest with potential applications in various areas such as statistics and system identifications [18,19,29].”
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].”
Infrared Small Target Detection via Non-Convex Rank Approximation Minimization Joint l2, 1 Norm (2018, background): “Similar to the nuclear norm, the l 1 norm gives every single element the same weight; this is a dilemma when there exist many strong edges and non-target sparse points.”
Phase Retrieval with Application to Optical Imaging: A contemporary overview (2015, methodology): “Alternatively, one may use the log-det reweighted rank minimization heuristic suggested in [97], which is the approach followed in [38] and [46].”
Phase Retrieval via Matrix Completion (2011, background): “However, it is possible to further promote low-rank solutions by solving a sequence of weighted trace-norm problems, a technique which has been shown to provide even more accurate solutions [26, 16].”
Iterative Reweighted 1 and 2 Methods for Finding Sparse Solutions (2010, methodology): “In general, if g(x i ) is concave in x 2 i , it can be handled using reweighted 2 [17], while any g(x i ) that is concave in |x i | can be used with reweighted 1 [9].”
RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images (2010, background): “choose to minimize a logdeterminant measure that can be viewed as a smooth surrogate for the rank function [10].”
Convex Optimization & Euclidean Distance Geometry (2004, background): “1 Rank minimization heuristic A remedy developed in [80] [175] [81] [79] introduces the convex envelope (cenv) of the quasiconcave rank function:”
Rank-Sparsity Incoherence for Matrix Decomposition (2009, background): “A low-rank Hankel matrix corresponds to a system with small model order and provides a minimal realization for a system [15].”