Geometry of reproducing kernels and information geometry with reproducing kernels
| Project/Area Number |
19740033
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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 |
Geometry
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
MATSUZOE Hiroshi Nagoya Institute of Technology, 大学院・工学研究科, 准教授 (90315177)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,890,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 情報幾何学 / 統計多様体 / 捩れをゆるす統計多様体 / アファイン微分幾何学 / アファイン分布 / q-正規分布 / q-指数型分布 / 再生核 / カーネル法 / アファイン接続 |
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| Research Abstract |
In this research, we studied reproducing kernels from the viewpoint of differential geometry and studied information geometry related to the theory of reproducing kernels. A nonlinear map to the feature space in the theory of reproducing kernels can be regarded as a map to the tangent space of a high-dimensional manifold. We applied this idea to information geometry, and we obtained several results of geometry of affine distributions. A map to the feature space induces geometric structures on the sample space of a statistical model. In order to elucidate the theory of reproducing kernels and information geometry, we studied geometry of Tsallis statistics.
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Report
(6 results)
Research Products
(50 results)
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[Presentation] Geometry of pre-contrast functions2010
Author(s)
Hiroshi Matsuzoe
Organizer
10th International Workshop on Complex Structures, Integrability and Vector Fields
Place of Presentation
Institute for Mathematics and Informatics, Bulgaria
Year and Date
2010-09-13
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