2010 Fiscal Year Final Research Report
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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| Keywords | 情報幾何学 / 統計多様体 |
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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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