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Approximate Regularization Paths for Nuclear Norm Minimization Using Singular Value Bounds -- With Implementation and Extended Appendix [article]

Niclas Blomberg, Cristian R. Rojas, Bo Wahlberg
<span title="2015-04-20">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune.  ...  In this paper, we extend the algorithm to provide error bounds for the singular values of the approximation. We exemplify the algorithms on large scale benchmark examples in model order reduction.  ...  The nuclear norm • * = i σ i (•), i.e., the sum of the singular values, is used as a convex surrogate for the non-convex rank function; this is so because the nuclear norm can be interpreted as a convex  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1504.05208v1">arXiv:1504.05208v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wjc57ydvgvgfrk6l2txsh4xccm">fatcat:wjc57ydvgvgfrk6l2txsh4xccm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191024205852/https://arxiv.org/pdf/1504.05208v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0a/a3/0aa3ec20fde6e00e3e195464aa530f9706570f9d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1504.05208v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Approximate regularization paths for nuclear norm minimization using singular value bounds

N. Blomberg, C.R. Rojas, B. Wahlberg
<span title="">2015</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nmirrnctcjfxfhkvzzso25hkey" style="color: black;">2015 IEEE Signal Processing and Signal Processing Education Workshop (SP/SPE)</a> </i> &nbsp;
The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune.  ...  In this paper, we extend the algorithm to provide error bounds for the singular values of the approximation. We exemplify the algorithms on large scale benchmark examples in model order reduction.  ...  The nuclear norm · * = i σ i (·), i.e., the sum of the singular values, is used as a convex surrogate for the non-convex rank function; this is so because the nuclear norm can be interpreted as a convex  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/dsp-spe.2015.7369551">doi:10.1109/dsp-spe.2015.7369551</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/dsp-spe/BlombergRW15.html">dblp:conf/dsp-spe/BlombergRW15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gizl6kuelrgg7lcunmly7hyo3u">fatcat:gizl6kuelrgg7lcunmly7hyo3u</a> </span>
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Linear system identification via atomic norm regularization

Parikshit Shah, Badri Narayan Bhaskar, Gongguo Tang, Benjamin Recht
<span title="">2012</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">2012 IEEE 51st IEEE Conference on Decision and Control (CDC)</a> </i> &nbsp;
We provide rigorous statistical guarantees that explicitly bound the estimation error (in the H 2 -norm) in terms of the stability radius, the Hankel singular values of the true system and the number of  ...  We pose a convex optimization problem that approximately solves the atomic norm minimization problem and identifies the unknown system from noisy linear measurements.  ...  In contrast, the atomic norm regularizer proposed in this paper is not only equivalent to the sum of the Hankel singular values (the Hankel nuclear norm), but is also well approximated by a finite dimensional  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2012.6426006">doi:10.1109/cdc.2012.6426006</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/ShahBTR12.html">dblp:conf/cdc/ShahBTR12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/opf2e6sl6ndqjgdxymfom5p3eu">fatcat:opf2e6sl6ndqjgdxymfom5p3eu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830042342/https://people.eecs.berkeley.edu/~brecht/papers/12.Sha.EtAl.Hankel.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2f/09/2f099e793bbeeb1750be87f11e03f9b7462f5c63.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2012.6426006"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Linear System Identification via Atomic Norm Regularization [article]

Parikshit Shah, Badri Narayan Bhaskar, Gongguo Tang, Benjamin Recht
<span title="2012-04-03">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We provide rigorous statistical guarantees that explicitly bound the estimation error (in the H_2-norm) in terms of the stability radius, the Hankel singular values of the true system and the number of  ...  We pose a convex optimization problem that approximately solves the atomic norm minimization problem and identifies the unknown system from noisy linear measurements.  ...  In contrast, the atomic norm regularizer proposed in this paper is not only equivalent to the sum of the Hankel singular values (the Hankel nuclear norm), but is also well approximated by a finite dimensional  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1204.0590v1">arXiv:1204.0590v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ufxhsxsthrfc5ez5pa5jaykdhq">fatcat:ufxhsxsthrfc5ez5pa5jaykdhq</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1204.0590/1204.0590.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1204.0590v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Reduced rank regression via adaptive nuclear norm penalization

K. Chen, H. Dong, K.-S. Chan
<span title="2013-09-11">2013</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6oeltljhrzfq7brjdtp2wqehpu" style="color: black;">Biometrika</a> </i> &nbsp;
We propose an adaptive nuclear norm penalization approach for low-rank matrix approximation, and use it to develop a new reduced rank estimation method for high-dimensional multivariate regression.  ...  The adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix, and it is generally non-convex under the natural restriction that the weight decreases with the singular value  ...  Acknowledgments We thank Howell Tong, and are grateful to an associate editor and two referees for constructive comments that helped improve the paper significantly.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/biomet/ast036">doi:10.1093/biomet/ast036</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/25045172">pmid:25045172</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4101086/">pmcid:PMC4101086</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mhtbt6nucrcarlxds3vcwzh47m">fatcat:mhtbt6nucrcarlxds3vcwzh47m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200503050642/http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC4101086&amp;blobtype=pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/45/00/450002b3692ef166731b3ea77aeab247bd1902e3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/biomet/ast036"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4101086" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Convergence bounds for nonlinear least squares and applications to tensor recovery [article]

Philipp Trunschke
<span title="2021-08-11">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Bounds for this quantity have been derived in a previous work and depend primarily on the model class and are not influenced positively by the regularity of the sought function.  ...  We reexamine the results of the previous paper and derive a new bound that is able to utilize the regularity of the sought function.  ...  Our code made use of the following Python packages: numpy, scipy, and matplotlib [31, 56, 36] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.05237v1">arXiv:2108.05237v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uc3a5my4p5dlhmvuzlrhm4n6di">fatcat:uc3a5my4p5dlhmvuzlrhm4n6di</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210814212122/https://arxiv.org/pdf/2108.05237v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f6/a9/f6a917a8c84eb8a8bfee54b09fd35d2adf26f426.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.05237v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Spectral Regularization Algorithms for Learning Large Incomplete Matrices

Rahul Mazumder, Trevor Hastie, Robert Tibshirani
<span title="2010-03-01">2010</span> <i title="CrossRef test prefix"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jknrc7cg5zdmzoiaibuemsqpfu" style="color: black;">Journal of machine learning research</a> </i> &nbsp;
Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm.  ...  With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter.  ...  We thank Stephen Boyd, Emmanuel Candes, Andrea Montanari, and Nathan Srebro for helpful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/21552465">pmid:21552465</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC3087301/">pmcid:PMC3087301</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ku2kbqnynzbp7ld5os46u6gsgi">fatcat:ku2kbqnynzbp7ld5os46u6gsgi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190214155824/http://web.stanford.edu:80/~hastie/Papers/mazumder10a.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d5/0b/d50b8793ba64bc31b0dfd144db020b2e544e74b7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3087301" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

An Extended Frank--Wolfe Method with "In-Face" Directions, and Its Application to Low-Rank Matrix Completion

Robert M. Freund, Paul Grigas, Rahul Mazumder
<span title="">2017</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q3xjdl4ok5hbzabogkpxxajhfy" style="color: black;">SIAM Journal on Optimization</a> </i> &nbsp;
We present computational guarantees for the new method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates.  ...  This is accomplished by a new approach to generating "in-face" directions at each iteration, as well as through new choice rules for selecting between inface and "regular" Frank-Wolfe steps.  ...  Recall that for a given Z ∈ R m×n , the sum of the singular values of Z is a norm often referred to as the nuclear norm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/15m104726x">doi:10.1137/15m104726x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h3j6or2wxfdhtexhosi7tva62a">fatcat:h3j6or2wxfdhtexhosi7tva62a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190304040051/http://pdfs.semanticscholar.org/d4d4/b6ac0f6031c673215a4d4fecb84091346f32.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d4/d4/d4d4b6ac0f6031c673215a4d4fecb84091346f32.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/15m104726x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

An Extended Frank-Wolfe Method with "In-Face" Directions, and its Application to Low-Rank Matrix Completion [article]

Robert M. Freund and Paul Grigas and Rahul Mazumder
<span title="2015-11-06">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present computational guarantees for the new method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates.  ...  This is accomplished by a new approach to generating "in-face" directions at each iteration, as well as through new choice rules for selecting between in-face and "regular" Frank-Wolfe steps.  ...  Recall that, for a given Z ∈ R m×n , the sum of the singular values of Z is a norm often referred to as the nuclear norm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1511.02204v1">arXiv:1511.02204v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/voyxihsflfdu3io7hqj7mveedy">fatcat:voyxihsflfdu3io7hqj7mveedy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826150221/https://arxiv.org/pdf/1511.02204v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b7/9e/b79e53542c8d2ceaa58d897d62e6d3ebfe99ec1f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1511.02204v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Reduced rank vector generalized linear models for feature extraction

Yiyuan She
<span title="">2013</span> <i title="International Press of Boston"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/op2nporwsjcpne4gikw3jf6pwm" style="color: black;">Statistics and its Interface</a> </i> &nbsp;
From the perspective of thresholding rules, we build a framework for fitting singular value penalized models and use it for feature extraction.  ...  Through solving the rank constraint form of the problem, we propose progressive feature space reduction for fast computation in high dimensions with little performance loss.  ...  ACKNOWLEDGEMENTS The author is grateful to the anonymous referee and the associate editor for their careful comments and useful suggestions. This work was partially supported by NSF grant CCF-1116447.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4310/sii.2013.v6.n2.a4">doi:10.4310/sii.2013.v6.n2.a4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hffk32bi75abvochw3sfa7lq3m">fatcat:hffk32bi75abvochw3sfa7lq3m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719114128/http://www.intlpress.com/site/pub/files/_fulltext/journals/sii/2013/0006/0002/SII-2013-0006-0002-a004.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6f/28/6f288a449444121591a5bf240baa447d13559270.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4310/sii.2013.v6.n2.a4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Low-Rank Optimization with Trace Norm Penalty

B. Mishra, G. Meyer, F. Bach, R. Sepulchre
<span title="">2013</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q3xjdl4ok5hbzabogkpxxajhfy" style="color: black;">SIAM Journal on Optimization</a> </i> &nbsp;
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates.  ...  To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold  ...  We thank the editor and two anonymous reviewers for carefully checking the paper and providing a number of helpful remarks.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/110859646">doi:10.1137/110859646</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u4t32dpdurazvbbksfrhbhwjpa">fatcat:u4t32dpdurazvbbksfrhbhwjpa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151022205307/https://hal.archives-ouvertes.fr/hal-00924110/file/lowrank_mishra_siopt.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e9/a9/e9a9cb267607234b977c197b57c83f244ee72a81.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/110859646"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Reduced rank regression via adaptive nuclear norm penalization [article]

Kun Chen, Hongbo Dong, Kung-Sik Chan
<span title="2012-09-23">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The adaptive nuclear norm is generally non-convex under the natural restriction that the weight decreases with the singular value.  ...  Adaptive nuclear-norm penalization is proposed for low-rank matrix approximation, by which we develop a new reduced-rank estimation method for the general high-dimensional multivariate regression problems  ...  Rank and nuclear norm penalized regression methods The fundamental results in Theorem 2.3 about rank and nuclear norm penalization for matrix approximation can be readily extended to the general regression  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1201.0381v2">arXiv:1201.0381v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hlzdvxqdevcfxcnqy4xccog6ca">fatcat:hlzdvxqdevcfxcnqy4xccog6ca</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1201.0381/1201.0381.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1201.0381v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Reduced Rank Vector Generalized Linear Models for Feature Extraction [article]

Yiyuan She
<span title="2012-05-09">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
From the perspective of thresholding rules, we build a framework for fitting singular value penalized models and use it for feature extraction.  ...  Through solving the rank constraint form of the problem, we propose progressive feature space reduction for fast computation in high dimensions with little performance loss.  ...  For example, P (t; λ) = λ|t| gives a multiple of the sum of singular values corresponding to the trace norm or nuclear norm penalty.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1007.3098v3">arXiv:1007.3098v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2tcw4senjjguxdf6m4dvwkuei4">fatcat:2tcw4senjjguxdf6m4dvwkuei4</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1007.3098/1007.3098.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/aa/e8/aae831a6387184804eaaa5a4c63e6ffe11f946ad.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1007.3098v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Dynamic Anomalography: Tracking Network Anomalies Via Sparsity and Low Rank

Morteza Mardani, Gonzalo Mateos, Georgios B. Giannakis
<span title="">2013</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/aznf273kcvcbfjcdeghr3xjd6i" style="color: black;">IEEE Journal on Selected Topics in Signal Processing</a> </i> &nbsp;
the sparsity-promoting ℓ_1-norm of the anomalies, and the nuclear norm of the nominal traffic matrix.  ...  After recasting the non-separable nuclear norm into a form amenable to online optimization, a real-time algorithm for dynamic anomalography is developed and its convergence established under simplifying  ...  The Frobenius norm of matrix is is the spectral norm, is the -norm, and is the nuclear norm, where denotes the -th singular value of .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/jstsp.2012.2233193">doi:10.1109/jstsp.2012.2233193</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ctasla2rm5fftpamwjkdutumge">fatcat:ctasla2rm5fftpamwjkdutumge</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130308195430/http://iie.fing.edu.uy:80/~gmateos/pubs/una/UNA_JSTSP.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2f/2f/2f2f6709149c013f87b1da715012c1cb65e67fd9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/jstsp.2012.2233193"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Large-Scale Low-Rank Matrix Learning with Nonconvex Regularizers [article]

Quanming Yao, James T.Kwok, Taifeng Wang, Tie-Yan Liu
<span title="2018-07-23">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we show that for many commonly-used nonconvex low-rank regularizers, a cutoff can be derived to automatically threshold the singular values obtained from the proximal operator.  ...  While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical performance.  ...  Obtaining an Approximate GSVT To obtain such a Q, we use the power method [27] (Algorithm 2) which has been recently used to approximate the SVT in nuclear norm minimization [15] , [17] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1708.00146v3">arXiv:1708.00146v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z7wy6ylpkjadfpmevvwjmemmgu">fatcat:z7wy6ylpkjadfpmevvwjmemmgu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200828152757/https://arxiv.org/pdf/1708.00146v2.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/92/98/92983d77c504d951a18c3ca6db4927eef03450b4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1708.00146v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
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