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We give the first input-sparsity time algorithms for the rank-$k$ low rank approximation problem in every Schatten norm.
Fast linear algebra is stable
James Demmel, Ioana Dumitriu, and Olga Holtz · 2007
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Robust PCA via outlier pursuit
Huan Xu, Constantine Caramanis, and Sujay Sanghavi · 2010
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Robust principal component analysis?
Emmanuel J. Candès, Xiaodong Li, Yi Ma, and John Wright · 2011
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Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression
Xiangrui Meng and Michael W. Mahoney · 2013
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OSNAP: Faster numerical linear algebra algorithms via sparser subspace embeddings
J. Nelson and H. L. Nguyen · 2013
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Sketching as a tool for numerical linear algebra
David P. Woodruff · 2014
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Dimensionality reduction for k k -means clustering and low rank approximation
Michael B. Cohen, Sam Elder, Cameron Musco, Christopher Musco, and Madalina Persu · 2015
Cited alongside, same era.
Uniform sampling for matrix approximation
Michael B. Cohen, Yin Tat Lee, Cameron Musco, Christopher Musco, Richard Peng, and Aaron Sidford · 2015
Cited alongside, same era.
Fast algorithms for robust PCA via gradient descent
Xinyang Yi, Dohyung Park, Yudong Chen, and Constantine Caramanis · 2016
Cited alongside, same era.
Input sparsity time low-rank approximation via ridge leverage score sampling
Michael B. Cohen, Cameron Musco, and Christopher Musco · 2017
Cited alongside, same era.
Low-rank approximation and regression in input sparsity time
Kenneth L. Clarkson and David P. Woodruff · 2017
Later among the works it cites.
Is input sparsity time possible for kernel low-rank approximation?
Cameron Musco and David P. Woodruff · 2017
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Faster linear algebra for data analysis and machine learning
Christopher Musco · 2018
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On approximating matrix norms in data streams
Yi. Li, Huy L. Nguyen, and David P. Woodruff · 2019
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