Iterative reweighted algorithms for matrix rank minimization

By Karthika Mohan, Maryam Fazel. Journal of machine learning research, 2012

380 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/043a92f1c350d979226a09d5882dcb65c4f8112f

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision (2016, methodology): “The Schatten-p norm minimization (SPNM) methods (Nie et al, 2012) (Mohan and Fazel, 2012) can also be understood as special cases of WNNM since the `p norm proximal problem can be solved by the iteratively thresholding method (She, 2012).”
Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm (2015, methodology): “In [28], [29], the Lp-norm of a vector is extended to the Schatten-p norm (0 < p < 1) and the iteratively reweighted least squares”
An Overview of Low-Rank Matrix Recovery From Incomplete Observations (2016, background): “The nuclear norm problems in (7) and (11) can also be minimized by solving a series of weighted least-squares problems, each of which can be solved using standard techniques for linear systems of equations [54,55,104].”
Generalized Nonconvex Nonsmooth Low-Rank Minimization (2014, neutral): “It has been recently extended to handle the nonconvex Schatten-p norm penalty [19].”
Accelerated Proximal Gradient Methods for Nonconvex Programming (2015, methodology): “Method name Assumption Accelerate (CP) converge (NCP) GD [16, 17] f + g: KL No Yes iPiano [18] nonconvex f , convex g No Yes GIST [19] nonconvex f , g = g1 − g2, g1, g2 convex No Yes GDPA [20] nonconvex f , g = g1 − g2, g1, g2 convex No Yes IR [8, 21] special f and g No Yes IFB [22] nonconvex f , no”
Stochastic Chebyshev Gradient Descent for Spectral Optimization (2018, background): “Examples include hyperparameter learning in Gaussian process regression with F ( X ) = log det X [23], nuclear norm regularization with F ( X ) = tr X 1 / 2 [21], phase retrieval with F ( X ) = tr ( X ) [9], and quantum state tomography with F ( X ) = tr ( X log X ) [16].”
Weighted Schatten $p$ -Norm Minimization for Image Denoising and Background Subtraction (2015, background): “Therefore, it has been proposed in [23], [28], [29], and [31] to enforce low rank regularization by using the Schatten p-norm, which is defined as the l p norm of the singular values ( ∑ i σ p i ) 1/p with 0 < p ≤ 1.”
A Globally Convergent Algorithm for Nonconvex Optimization Based on Block Coordinate Update (2014, background): “For example, KSVD [1] only has nonincreasing monotonicity of its objective sequence, and iterative reweighted algorithms for sparse and low-rank recovery in [15, 28, 35] only has subsequence convergence.”