OptShrink swMATH ID: 33657 Software Authors: Nadakuditi, Raj Rao Description: OptShrink: an algorithm for improved low-rank signal matrix denoising by optimal, data-driven singular value shrinkage. OptShrink is a simple, completely data-driven algorithm for denoising a low-rank signal matrix buried in noise. It takes as its input the signal-plus-noise matrix, an estimate of the signal matrix rank and returns as an output the improved signal matrix estimate. It computes this estimate by shrinking the singular values corresponding to the Truncated SVD (TSVD) in the correct manner as given by random matrix theory. It can be used in the missing data setting and for a large class of noise models for which the i.i.d. Gaussian setting is a special case. There are no tuning parameters involved so it can be used in a black-box manner wherever improving low-rank matrix estimation is desirable. The algorithm outperforms the truncated SVD (TSVD) significantly in the low to moderate SNR regime and will never do worse than the TSVD. The theory also explains why it will always do better than singular value thresholding. Homepage: https://web.eecs.umich.edu/~rajnrao/optshrink/ Dependencies: Matlab Related Software: SPECTRODE; ePCA; Pyglrm; LowRankModels; QuEST; softImpute; RMTool; Mcmcpack; WordNet; ElemStatLearn; nFactors; PROPACK; DLMF; odmd; BSSasymp; JADE; BRENT; leapp; Condor; DEseq Cited in: 21 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year OptShrink: an algorithm for improved low-rank signal matrix denoising by optimal, data-driven singular value shrinkage. Zbl 1360.62399Nadakuditi, Raj Rao 2014 all top 5 Cited by 24 Authors 5 Dobriban, Edgar 4 Leeb, William E. 2 Bigot, Jéremie 2 Deledalle, Charles-Alban 2 Ding, Xiucai 2 Nadakuditi, Raj Rao 2 Singer, Amit 1 Balzano, Laura 1 Chatterjee, Sourav 1 Cordero-Grande, Lucilio 1 Féral, Delphine 1 Fessler, Jeffrey A. 1 Hong, David 1 Johnstone, Iain Murray 1 Lazzaro, Damiana 1 Lettau, Martin 1 Liu, Lydia T. 1 Morigi, Serena 1 Onatski, Alexei 1 Owen, Art B. 1 Pelger, Markus 1 Prasadan, Arvind 1 Yang, Fan 1 Zhang, Anru R. all top 5 Cited in 15 Serials 6 The Annals of Statistics 2 Computational Statistics and Data Analysis 1 IEEE Transactions on Information Theory 1 Journal of Econometrics 1 Journal of Multivariate Analysis 1 Statistics & Probability Letters 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Bernoulli 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 Journal of Machine Learning Research (JMLR) 1 SIAM Journal on Applied Dynamical Systems 1 The Annals of Applied Statistics 1 Random Matrices: Theory and Applications 1 SIAM Journal on Mathematics of Data Science all top 5 Cited in 9 Fields 18 Statistics (62-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 7 Probability theory and stochastic processes (60-XX) 6 Information and communication theory, circuits (94-XX) 3 Numerical analysis (65-XX) 1 Combinatorics (05-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) Citations by Year