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We develop two approaches for analyzing the approximation error bound for the Nystr\"{o}m method, one based on the concentration inequality of integral operator, and one based on the compressive sensing theory.
Using the nystrom method to speed up kernel machines
Christopher Williams and Matthias Seeger · 2001
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Local rademacher complexities
Peter L. Bartlett, Olivier Bousquet, and Shahar Mendelson · 2002
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Global versus local methods in nonlinear dimensionality reduction
Vin De Silva and Joshua B Tenenbaum · 2003
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Spectral grouping using the nystrom method
Charless Fowlkes, Serge Belongie, Fan Chung, and Jitendra Malik · 2004
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Fast embedding of sparse music similarity graphs
John C. Platt · 2004
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On the nystrom method for approximating a gram matrix for improved kernel-based learning
Petros Drineas and Michael W. Mahoney · 2005
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Support vector machines on a budget
Ofer Dekel and Yoram Singer · 2006
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Compressed sensing
David L. Donoho · 2006
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Determinantal processes and independence
J. Ben Hough, Manjunath Krishnapur, Yuval Peres, and Balint Virag · 2006
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Sparsity and incoherence in compressive sampling
Emmanuel Candés and Justin Romberg · 2007
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Large-scale manifold learning
Ameet Talwalkar, Sanjiv Kumar, and Henry A. Rowley · 2008
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Improved nystrom low-rank approximation and error analysis
Kai Zhang, Ivor W. Tsang, and James T. Kwok · 2008
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Spectral methods in machine learning and new strategies for very large data sets
M.-A. Belabbas and P. J. Wolfe · 2009
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Sparse kernel svms via cutting-plane training
Thorsten Joachims and Chun-Nam John Yu · 2009
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Sampling techniques for the nystrom method
S. Kumar, M. Mohri, and A. Talwalkar · 2009
Cited alongside, same era.
Making large-scale nyström approximation possible
Mu Li, James T. Kwok, and Bao-Liang Lu · 2010
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Matrix coherence and the nystrom method
Ameet Talwalkar and Afshin Rostamizadeh · 2010
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The spectral norm error of the naive nystrom extension
Alex Gittens · 2011
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The local rademacher complexity of lp-norm multiple kernel learning
Marius Kloft and Gilles Blanchard · 2011
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Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems
Vladimir Koltchinskii · 2011
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Divide-and-conquer matrix factorization
Lester W. Mackey, Ameet S. Talwalkar, and Michael I. Jordan · 2011
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Geometry on probability spaces
Steve Smale and Ding-Xuan Zhou · 2009
Cited alongside, same era.
On the impact of kernel approximation on learning accuracy
Corinna Cortes, Mehryar Mohri, and Ameet Talwalkar · 2010
Cited alongside, same era.
Sparsity in multiple kernel learning
Vladimir Koltchinskii and Ming Yuan · 2010
Cited alongside, same era.
Randomized algorithms for matrices and data
Michael W. Mahoney · 2011
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A simple algorithm for semi-supervised learning with improved generalization error bound
Ming Ji, Tianbao Yang, Binbin Lin, Rong Jin, and Jiawei Han · 2012
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