A Note on Learning with Integral Operators
Abstract
A large number of learning algorithms, for example, spectral clustering, kernel Principal Components Analysis and many manifold methods, are based on estimating eigenvalues and eigenfunctions of operators defined by a similarity function or a kernel, given empirical data. Thus for the analysis of algorithms, it is an important problem to be able to assess the quality of such approximations. The contribution of our paper is two-fold: 1. We use a technique based on a concentration inequality for Hilbert spaces to provide new much simplified proofs for a number of results in spectral approximation. 2. Using these methods we provide several new results for estimating spectral properties of the graph Laplacian operator extending and strengthening results from [27].
Cite
Text
Rosasco et al. "A Note on Learning with Integral Operators." Annual Conference on Computational Learning Theory, 2009.Markdown
[Rosasco et al. "A Note on Learning with Integral Operators." Annual Conference on Computational Learning Theory, 2009.](https://mlanthology.org/colt/2009/rosasco2009colt-note/)BibTeX
@inproceedings{rosasco2009colt-note,
title = {{A Note on Learning with Integral Operators}},
author = {Rosasco, Lorenzo and Belkin, Mikhail and De Vito, Ernesto},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2009},
url = {https://mlanthology.org/colt/2009/rosasco2009colt-note/}
}