| Project/Area Number |
21540105
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tohoku University |
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Principal Investigator |
AKAMA Yohji 東北大学, 大学院・理学研究科, 准教授 (30272454)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | VC次元 / 連結成分 / 順序型 / 整列擬順序 / 連続変形 / better quasi-ordering / unbounded unions / set systems / deformation / order type / finite elasticity / inductive inference / better elasticity / 集合系 / well quasi-order / order-type / 組み合わせ次元 / 主成分分析 / Wishart行列の固有値 / 一致性 / 測度集中現象 / 有限の弾力性 / 可換正規シャッフル言語 / 結晶格子 |
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| Research Abstract |
By studying evaluation methods of the number of connected components of manifolds, we evaluated the VC dimensions of principal component analysis, as statistical learning. Next, we introduce a new order type of set systems to measure the difficulty to learn. We proved (1)any well quasi-ordering can be represented by a set system having our order type ; and (2)if a set system has our order type, then a continuous image of it by a Cantor monotone function does so. Finally, we developed the theory of our order type of set systems to the theory of better quasi-orderings.
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