On efficient configuration in multidimensional scaling

2017 Fiscal Year Final Research Report

• 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