The Optimal Hard Threshold for Singular Values is $4/\sqrt {3}$

By Matan Gavish, David L. Donoho. 2014

490 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistics and Probability, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Statistics and Probability

In Signal Processing

Citations in the corpus

Rejoinder on: Minimal penalties and the slope heuristics: a survey. (2019, methodology): “At least, in the Gaussian case, such a procedure could be used for estimating σ , even if other strategies exist (Gavish and Donoho, 2014, Section III.”
Multiresolution Dynamic Mode Decomposition (2015, methodology): “A principled way to truncate noisy data would be to use the recent hard-thresholding algorithm of Gavish and Donoho [18].”
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics (2020, methodology): “This approach is non-convex, relying on the alternating directions method (ADM) [47,52], and null space computations are highly ill-conditioned for noisy data [1,47,62], thus inspiring the current work and mathematical innovations.”
Randomized Matrix Decompositions using R (2016, methodology): “A computational intensive approach to determine the optimal number of components is via cross-validation approximations (Josse and Husson 2012), while a mathematically reﬁned approach is the optimal hard threshold method for singular values, formulated by Gavish and Donoho (2014).”
Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition. (2014, background): “The estimation of a truncation dimensionality r to best capture signal and reject noise in a dataset is the subjective of an extensive literature (for instance, [24, 25]).”
Matrix estimation by Universal Singular Value Thresholding (2012, background): “The recent paper [47] has explored the issue of attaining the minimax error all the way up to the correct constant.”
Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics (2016, methodology): “SIAM Journal on Matrix Analysis and Applications, 31(4):1621–1641.”
Bi-cross-validation for factor analysis (2015, background): “Donoho and Gavish [15] propose a hard-thresholding rule for the empirical singular values of the data that also accounts for this higher threshold.”