Mercer’s theorem, feature maps, and smoothing

Authors:
Ha Quang Minh;Partha Niyogi;Yuan Yao
Affiliations:
Department of Computer Science, University of Chicago, Chicago, IL;Department of Computer Science, University of Chicago, Chicago, IL;Department of Mathematics, University of California, Berkeley, Berkeley, CA
Venue:
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Year:
2006

Citing 4
Cited 15

The covering number in learning theory

Journal of Complexity
Semi-Supervised Learning on Riemannian Manifolds

Machine Learning
Diffusion Kernels on Statistical Manifolds

The Journal of Machine Learning Research
Model Selection for Regularized Least-Squares Algorithm in Learning Theory

Foundations of Computational Mathematics

Causal reasoning by evaluating the complexity of conditional densities with kernel methods

Neurocomputing
Active Learning by Spherical Subdivision

The Journal of Machine Learning Research
Integral operators on the sphere generated by positive definite smooth kernels

Journal of Complexity
An MRF-based kernel method for nonlinear feature extraction

Image and Vision Computing
Image and Video Colorization Using Vector-Valued Reproducing Kernel Hilbert Spaces

Journal of Mathematical Imaging and Vision
SVM-based supervised and unsupervised classification schemes

WSEAS Transactions on Computers
Exploiting long-range dependencies in protein β-sheet secondary structure prediction

PRIB'10 Proceedings of the 5th IAPR international conference on Pattern recognition in bioinformatics
The analysis of a faster algorithm for support vector machine-based classification

ICCOMP'10 Proceedings of the 14th WSEAS international conference on Computers: part of the 14th WSEAS CSCC multiconference - Volume I
A general frame for building optimal multiple SVM kernels

LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Learning to classify service data with latent semantics

RSKT'12 Proceedings of the 7th international conference on Rough Sets and Knowledge Technology
Change detection based on a support vector data description that treats dependency

Pattern Recognition Letters
An explicit description of the extended gaussian kernel

PAKDD'12 Proceedings of the 2012 Pacific-Asia conference on Emerging Trends in Knowledge Discovery and Data Mining
Translation Invariance in the Polynomial Kernel Space and Its Applications in kNN Classification

Neural Processing Letters
Full length article: Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

Journal of Approximation Theory
A general non-local denoising model using multi-kernel-induced measures

Pattern Recognition

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study Mercer’s theorem and feature maps for several positive definite kernels that are widely used in practice. The smoothing properties of these kernels will also be explored.