A Note on Perturbation Results for Learning Empirical Operators
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 alg...
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2008
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| Online Access: | http://hdl.handle.net/1721.1/41940 |
| _version_ | 1826199312336420864 |
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| author | De Vito, Ernesto Belkin, Mikhail Rosasco, Lorenzo |
| author2 | Tomaso Poggio |
| author_facet | Tomaso Poggio De Vito, Ernesto Belkin, Mikhail Rosasco, Lorenzo |
| author_sort | De Vito, Ernesto |
| collection | MIT |
| description | 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 [26]. |
| first_indexed | 2024-09-23T11:18:09Z |
| id | mit-1721.1/41940 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:18:09Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | mit-1721.1/419402019-04-12T09:57:55Z A Note on Perturbation Results for Learning Empirical Operators De Vito, Ernesto Belkin, Mikhail Rosasco, Lorenzo Tomaso Poggio Center for Biological and Computational Learning (CBCL) perturbation theory statistical learning theory kernel methods spectral methods 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 [26]. 2008-08-20T19:15:07Z 2008-08-20T19:15:07Z 2008-08-19 http://hdl.handle.net/1721.1/41940 MIT-CSAIL-TR-2008-052 CBCL-274 Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Unported http://creativecommons.org/licenses/by-nc-nd/3.0/ 22 p. application/pdf application/postscript |
| spellingShingle | perturbation theory statistical learning theory kernel methods spectral methods De Vito, Ernesto Belkin, Mikhail Rosasco, Lorenzo A Note on Perturbation Results for Learning Empirical Operators |
| title | A Note on Perturbation Results for Learning Empirical Operators |
| title_full | A Note on Perturbation Results for Learning Empirical Operators |
| title_fullStr | A Note on Perturbation Results for Learning Empirical Operators |
| title_full_unstemmed | A Note on Perturbation Results for Learning Empirical Operators |
| title_short | A Note on Perturbation Results for Learning Empirical Operators |
| title_sort | note on perturbation results for learning empirical operators |
| topic | perturbation theory statistical learning theory kernel methods spectral methods |
| url | http://hdl.handle.net/1721.1/41940 |
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