Matrix analysis
Kernel principal component analysis
Advances in kernel methods
Ridge Regression Learning Algorithm in Dual Variables
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
The Effect of the Input Density Distribution on Kernel-based Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Accurate Error Bounds for the Eigenvalues of the Kernel Matrix
The Journal of Machine Learning Research
Link analysis, eigenvectors and stability
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 2
On the eigenspectrum of the gram matrix and the generalization error of kernel-PCA
IEEE Transactions on Information Theory
Eigenvalues perturbation of integral operator for kernel selection
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
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The eigenvalues of the kernel matrix play an important role in a number of kernel methods. It is well known that these eigenvalues converge as the number of samples tends to infinity. We derive a probabilistic finite sample size bound on the approximation error of an individual eigenvalue, which has the important property that the bound scales with the dominate eigenvalue under consideration, reflecting the accurate behavior of the approximation error as predicted by asymptotic results and observed in numerical simulations. Under practical conditions, the bound presented here forms a significant improvement over existing non-scaling bound. Applications of this theoretical finding in kernel matrix selection and kernel target alignment are also presented.