A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The weighted majority algorithm
Information and Computation
Machine Learning
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
Latent semantic indexing: a probabilistic analysis
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Sparse Greedy Matrix Approximation for Machine Learning
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Fast Monte-Carlo Algorithms for finding low-rank approximations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The CMU Pose, Illumination, and Expression (PIE) Database
FGR '02 Proceedings of the Fifth IEEE International Conference on Automatic Face and Gesture Recognition
Efficient svm training using low-rank kernel representations
The Journal of Machine Learning Research
Kernel independent component analysis
The Journal of Machine Learning Research
Spectral Grouping Using the Nyström Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Predictive low-rank decomposition for kernel methods
ICML '05 Proceedings of the 22nd international conference on Machine learning
Matrix approximation and projective clustering via volume sampling
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
SIAM Journal on Computing
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Journal of the ACM (JACM)
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
The Journal of Machine Learning Research
Fast computation of low-rank matrix approximations
Journal of the ACM (JACM)
Sampling from large matrices: An approach through geometric functional analysis
Journal of the ACM (JACM)
Stability of transductive regression algorithms
Proceedings of the 25th international conference on Machine learning
Improved Nyström low-rank approximation and error analysis
Proceedings of the 25th international conference on Machine learning
Relative-Error $CUR$ Matrix Decompositions
SIAM Journal on Matrix Analysis and Applications
Density-weighted nyström method for computing large kernel eigensystems
Neural Computation
An improved approximation algorithm for the column subset selection problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On sampling-based approximate spectral decomposition
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
Accelerated dense random projections
Accelerated dense random projections
A Randomized Algorithm for Principal Component Analysis
SIAM Journal on Matrix Analysis and Applications
An experimental evaluation of a Monte-Carlo algorithm for singular value decomposition
PCI'01 Proceedings of the 8th Panhellenic conference on Informatics
Sub-sampling for efficient spectral mesh processing
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
A fast random sampling algorithm for sparsifying matrices
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Large scale online kernel classification
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Reduced heteroscedasticity linear regression for Nyström approximation
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Improving CUR matrix decomposition and the Nyström approximation via adaptive sampling
The Journal of Machine Learning Research
Large-scale SVD and manifold learning
The Journal of Machine Learning Research
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The Nyström method is an efficient technique to generate low-rank matrix approximations and is used in several large-scale learning applications. A key aspect of this method is the procedure according to which columns are sampled from the original matrix. In this work, we explore the efficacy of a variety of fixed and adaptive sampling schemes. We also propose a family of ensemble-based sampling algorithms for the Nyström method. We report results of extensive experiments that provide a detailed comparison of various fixed and adaptive sampling techniques, and demonstrate the performance improvement associated with the ensemble Nyström method when used in conjunction with either fixed or adaptive sampling schemes. Corroborating these empirical findings, we present a theoretical analysis of the Nyström method, providing novel error bounds guaranteeing a better convergence rate of the ensemble Nyström method in comparison to the standard Nyström method.