Ordering structure of Euclidean distance matrices with applications to statistical multidimensional scaling

欧几里得距离矩阵的排序结构及其在统计多维标度中的应用

• 批准号: 21500272
• 负责人: KURATA Hiroshi
• 金额: $ 2.83万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21500272/
• 关键词: 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; 固有値; 非負値定符号行列

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.

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矩阵（3）作者研究了细胞基质的某些特性，这些特性是特殊的欧几里得距离矩阵。（4）作者在线性子空间上得出了一些新的结果，其中一组多元混合物分布的主要点。

项目成果

Multispherical Euclidean distance matrices

多球欧几里得距离矩阵

• 发表时间: 2010
• 期刊: Linear Algebra and Its Applications
• 影响因子: 1.1
• 作者: Hiroshi KURATA;and Pablo TARAZAGA
• 通讯作者: and Pablo TARAZAGA

Definition and properties of m-dimensional n-principal points

m维n主点的定义和性质

• 发表时间: 2012
• 期刊: Communications in Statistics-Theory and Methods
• 影响因子: 0.8
• 作者: Shun Matsuura;Hiroshi Kurata
• 通讯作者: Hiroshi Kurata

A principal subspace theorem for 2-principal points of a general location mixture of snherically symmetric distributions

球对称分布一般位置混合的2主点的主子空间定理

• 发表时间: 2010
• 期刊: Statistics and Probability Letters
• 影响因子: 0.8
• 作者: Shun Matsuura;Hiroshi Kurata
• 通讯作者: Hiroshi Kurata

Principal points of a multivariate mixture distribution

• DOI: 10.1016/j.jmva.2010.08.009
• 发表时间: 2011-02
• 期刊: J. Multivar. Anal.
• 作者: S. Matsuura;H. Kurata

A principal subspace theorem for 2-principal points of a general location mixture of spherically symmetric distributions

球对称分布一般位置混合的 2 主点的主子空间定理

• 发表时间: 2010
• 期刊: Statistics and Probability Letters
• 影响因子: 0.8
• 作者: M.Kuroda;H.Hashiguchi;S.Nakagawa.;Shun MATSUURA and Hiroshi KURATA
• 通讯作者: Shun MATSUURA and Hiroshi KURATA