Machine Learning
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
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
Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
The Journal of Machine Learning Research
Improved Nyström low-rank approximation and error analysis
Proceedings of the 25th international conference on Machine learning
Density-weighted nyström method for computing large kernel eigensystems
Neural Computation
A fast dual method for HIK SVM learning
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Sampling methods for the Nyström method
The Journal of Machine Learning Research
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The Nyström method is a well known sampling based low-rank matrix approximation approach. It is usually considered to be originated from the numerical treatment of integral equations and eigendecomposition of matrices. In this paper, we present a novel point of view for the Nyström approximation. We show that theoretically the Nyström method can be regraded as a set of point-wise ordinary least square linear regressions of the kernel matrix, sharing the same design matrix. With the new interpretation, we are able to analyze the approximation quality based on the fulfillment of the homoscedasticity assumption and explain the success and deficiency of various sampling methods. We also empirically show that positively skewed explanatory variable distributions can lead to heteroscedasticity. Based on this discovery, we propose to use non-symmetric explanatory functions to improve the quality of the Nyström approximation with almost no extra computational cost. Experiments show that positively skewed datasets widely exist, and our method exhibits good improvements on these datasets.