2011 Fiscal Year Final Research Report
Ordering structure of Euclidean distance matrices with applications to statistical multidimensional scaling
| Project/Area Number |
21500272
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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 |
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・総合文化研究科, 准教授 (50284237)
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| Project Period (FY) |
2009 – 2011
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| Keywords | マジョライゼーション / ユークリッド距離行列 / 多次元尺度構成法 / 置換行列群 |
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| Research Abstract |
The results of this research are summarized as follows:
(1) Some new results on the characterization of multi-spherical Euclidean distance matrices were derived.
(2) The authors showed that if the eigenvalues of a centered positive semidefinite matrix majorizes those of another centered positive semidefinite matrix, then the same inequality holds for the eigenvalues of the corresponding two Euclidean distance matrices.
(3) The authors investigated some properties of cell matrices, which are special Euclidean distance matrices.
(4) The authors derived some new results on the linear subspace in which a set of principal points of a multivariate mixture distribution.
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