| Presentation | 2002/10/10 Generalization Error Analysis for Polynomial Kernel Methods : Algebraic Geometrical Approach Kazushi IKEDA, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The generalization properties of learning classifiers with a polynomial kernel function are examined here. We first show that the generalization error of the learning machine depends on the properties of the separating curve, the intersection of the input surface defined as the submanifold made of the input vectors in the feature space and the true separating hyperplane. When the input space is one-dimensional, the problem is decomposed to as many one-dimensional problems as the number of the intersecting points. Otherwise, the generalization error is determined by the class of the separating curve. Next, we consider how the class of the separating curve depends on the true separating function. The class is maximum when the true separating polynomial function is irreducible and smaller otherwise. In either case, the class depends only on the true function and does not on the dimension of the feature space. The results imply that the generalization error does not increase even when the dimension of the feature space gets larger and that the so-called overfitting does not occur in the kernel learning. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Generalization Error / Kernel Methods / Algebraic Geometry |
| Paper # | NC2002-51 |
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| Committee | NC |
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| Conference Date | 2002/10/10(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Neurocomputing (NC) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Generalization Error Analysis for Polynomial Kernel Methods : Algebraic Geometrical Approach |
| Sub Title (in English) | |
| Keyword(1) | Generalization Error |
| Keyword(2) | Kernel Methods |
| Keyword(3) | Algebraic Geometry |
| 1st Author's Name | Kazushi IKEDA |
| 1st Author's Affiliation | Kyoto University() |
| Date | 2002/10/10 |
| Paper # | NC2002-51 |
| Volume (vol) | vol.102 |
| Number (no) | 381 |
| Page | pp.pp.- |
| #Pages | 4 |
| Date of Issue | |