Information geometric approach to singular structure of the family of probability distributions on shape spaces

2016 Fiscal Year Final Research Report

• Project/Area Number: 26540013
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: The University of Tokyo (2015-2016); Keio University (2014)
• Principal Investigator: SEI TOMONARI 東京大学, 大学院情報理工学系研究科, 准教授 (20401242)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: テキスタイル集合 / 情報幾何 / 微分幾何 / 総合指数 / textile plot / シェイプ空間

Outline of Final Research Achievements

We obtained three main results about statistical inference on shapes, where a shape is a sequence of spatial points under identification with respect to parallel displacement, rotation and scaling. First, we defined a set called the textile set related to the shape space, and elucidated its geometric properties. Secondly, we derived differential equations satisfied by the normalizing constant of spherical distributions on the sphere. Finally, we proposed a method of determining an objective general index. The results are presented through international conferences and journal papers.

Free Research Field

統計学