2017 Fiscal Year Final Research Report
On efficient configuration in multidimensional scaling
Project/Area Number |
26330035
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Statistical science
|
Research Institution | The University of Tokyo |
Principal Investigator |
Kurata Hiroshi 東京大学, 大学院情報学環, 教授 (50284237)
|
Project Period (FY) |
2014-04-01 – 2018-03-31
|
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 |
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.
|
Free Research Field |
統計科学
|