2011 Fiscal Year Final Research Report
Mathematical Properties of Sampling and Optimal Reproducing Kernels
| Project/Area Number |
21700001
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Hokkaido University |
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Principal Investigator |
TANAKA Akira 北海道大学, 大学院・情報科学研究科, 准教授 (20332471)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 情報数理 / 標本化定理 / 再生核ヒルベルト空間 / 機械学習 |
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| Research Abstract |
In this work, we theoretically analyzed properties of sampling theories for reproducing kernel Hilbert spaces(RKHS's). Our main contributions are1) we gave a necessary and sufficient condition for a given RKHS and a given set of sampling points to satisfy the sampling theorem, 2) we gave an upper bound of errors in case that the sampling theorem does not hold, and3) we clarified the behavior of the solution in various machine learning problems with respect to sampling points and an adopted RKHS.
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