New developments of statistical data analysis with algebraic topology
| Project/Area Number |
26540016
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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 Institute of Statistical Mathematics |
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Principal Investigator |
Fukumizu Kenji 統計数理研究所, 数理・推論研究系, 教授 (60311362)
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| Co-Investigator(Kenkyū-buntansha) |
平岡 裕章 東北大学, 原子分子材料科学高等研究機構, 教授 (10432709)
栗木 哲 統計数理研究所, 数理・推論研究系, 教授 (90195545)
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| Co-Investigator(Renkei-kenkyūsha) |
MATSUE Kaname 九州大学, マス・フォア・インダストリ研究所, 助教 (70610046)
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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: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 多変量解析 / 代数的位相幾何 / 多様体学習 / 統計的位相幾何 / 代数的位相帰化 |
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| Outline of Final Research Achievements |
(1) Kernel methods for vectorizing persitence diagrams has been proposed, and they have been applied to detecting the phase transition temperature between glass and liquid. (2) A framework for phyogeny analysis has been proposed based on manifold learning and gene clustering. (3) The method of Euler number has been applied to derive reliability intervals of regression problems as well as the distribution of maximum eigenvalue of random matrices.
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Report
(4 results)
Research Products
(23 results)
