On efficient configuration in multidimensional scaling
| Project/Area Number |
26330035
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Kurata Hiroshi 東京大学, 大学院情報学環, 教授 (50284237)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 多次元尺度構成法 / ユークリッド距離行列 / 一般逆行列 / 行列の順序 / Moore-Penrose 一般逆行列 / 非類似度行列 / core inverse / core partial ordering / セル行列 / ムーア・ペンローズ逆行列 / ラプラシアン |
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| Outline of Final Research Achievements |
In this research, I discussed the problem of constructing efficient configuration in multidimensional scaling. In particular, I studied some properties of Euclidean distance matrices (EDMs) in detail. First I focused on a class of cell matrices, which is a subset of EDMs and has a very simple strucuture. Since the class has various potential applications to real data analysis, I studied its properties from geometric and linear algebraic points of view. Next I derived a general expression for the EDM closest to a given cell matrix and the Moore-Penrose inverse of an EDM. Both results give a theoretic basis for efficient configuration in multidimnsional scaling. I also defined a prodct on the set of EDMs and studied its properties.
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Report
(5 results)
Research Products
(18 results)
