Discrete and continuous multivariate analysis of symmetry for high dimensional data

2020 Fiscal Year Final Research Report

• Project/Area Number: 18K03425
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Tokyo University of Science
• Principal Investigator: Tomizawa Sadao 東京理科大学, 理工学部情報科学科, 教授 (50188778)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Keywords: 分割表統計解析

Outline of Final Research Achievements

In statistics, we considered (1) the model of symmetry, its decomposition and the measure in the descrete multivariate analysis , and (2) the structure of symmetry of the probability density function and the decomposition of them in the continuous multivariate analysis. We then considered the fusion of the symmetric structures of discrete and continuous multivariate analysis.
We considerd a multivariate contingency table analysis method for symmetry for multivariate data, when continuous data originally follows a potential continuous multivariate distribution, when a high-dimensional contingency table is constructed with cut points.
Considering the relationship of the symmetry structures, we constructed a high-dimensional multivariate analysis method that is a fusion of discrete and continuous.

Free Research Field

数理統計学

Academic Significance and Societal Importance of the Research Achievements

本研究で提案した多次元データ解析に対応する離散と連続の多変量解析における対称性に関する新しい解析法は，教育，心理，社会学，経済，理学，医薬などの種々の応用分野における実際の多変量データ解析に適用可能で，特に，ビッグデータのような高次元データの解析に具体的にも寄与するところが大きい．提案する方法は，国内外においてまだ提案されていない全くの新しい解析法であり，極めて独創的であり，国内外の離散と連続の多変量解析の融合の研究に非常に大きく貢献するものといえる．