Thery and methods for high dimensional data analysis with internal structure

2018 Fiscal Year Final Research Report

• Project/Area Number: 26280009
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Fukumizu Kenji 統計数理研究所, 数理・推論研究系, 教授 (60311362)
• Co-Investigator(Kenkyū-buntansha): 鈴木 大慈 東京大学, 大学院情報理工学系研究科, 准教授 (60551372) ; 小林 景 慶應義塾大学, 理工学部(矢上), 准教授 (90465922)
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: 統計数学 / データ解析 / 高次元 / アルゴリズム

Outline of Final Research Achievements

The hub phenomenon has been analysed as an example of special properties of high-dimensional data, and a method of resolving hubs has been proposed. Methods of data analysis have been proposed for non-Euclidean data such as trees and points with skewed distance measures. Additionally, for a new method of density estimation of high-dimensional data, a kernel methods for constructing infinite dimensional exponential families has been proposed, and its estmation has been discussed.

Free Research Field

機械学習

Academic Significance and Societal Importance of the Research Achievements

ビッグデータ時代になり高次元で複雑なデータを扱う必要性が高まったが，そのようなデータの性質や解析法の関して，理論的な知見や有効な方法が成果として得られた．今後，さまざまな分野に現れる高次元データを扱う際にこれらの成果が貢献できると考える．