| Project/Area Number |
26540013
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Statistical science
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| Research Institution | The University of Tokyo (2015-2016)
Keio University (2014) |
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Principal Investigator |
SEI TOMONARI 東京大学, 大学院情報理工学系研究科, 准教授 (20401242)
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| Co-Investigator(Kenkyū-buntansha) |
田中 潮 大阪府立大学, 理学(系)研究科(研究院), 助教 (60516897)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | テキスタイル集合 / 情報幾何 / 微分幾何 / 総合指数 / textile plot / シェイプ空間 / 可微分多様体 / ホロノミック勾配法 / 客観的総合指数 / 国際研究者交流 / イギリス |
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| Outline of Final Research Achievements |
We obtained three main results about statistical inference on shapes, where a shape is a sequence of spatial points under identification with respect to parallel displacement, rotation and scaling. First, we defined a set called the textile set related to the shape space, and elucidated its geometric properties. Secondly, we derived differential equations satisfied by the normalizing constant of spherical distributions on the sphere. Finally, we proposed a method of determining an objective general index. The results are presented through international conferences and journal papers.
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