Machine Learning
Least Squares Support Vector Machine Classifiers
Neural Processing Letters
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Proximal support vector machine classifiers
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Lagrangian support vector machines
The Journal of Machine Learning Research
epsilon-SSVR: A Smooth Support Vector Machine for epsilon-Insensitive Regression
IEEE Transactions on Knowledge and Data Engineering
Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication
SIAM Journal on Computing
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
SIAM Journal on Computing
SIAM Journal on Computing
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
The Journal of Machine Learning Research
Nonlinear Dimension Reduction with Kernel Sliced Inverse Regression
IEEE Transactions on Knowledge and Data Engineering
Robust kernel principal component analysis
Neural Computation
Active set support vector regression
IEEE Transactions on Neural Networks
Reduced Support Vector Machines: A Statistical Theory
IEEE Transactions on Neural Networks
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Many kernel-based learning algorithms have the computational load scaled with the sample size n due to the column size of a full kernel Gram matrix K. This article considers the Nystrom low-rank approximation. It uses a reduced kernel K@^, which is nxm, consisting of m columns (say columns i"1,i"2,...,i"m) randomly drawn from K. This approximation takes the form K~K@^U^-^1K@^^T, where U is the reduced mxm matrix formed by rows i"1,i"2,...,i"m of K@^. Often m is much smaller than the sample size n resulting in a thin rectangular reduced kernel, and it leads to learning algorithms scaled with the column size m. The quality of matrix approximations can be assessed by the closeness of their eigenvalues and eigenvectors. In this article, asymptotic error bounds on eigenvalues and eigenvectors are derived for the Nystrom low-rank approximation matrix.