New developments of statistical data analysis with algebraic topology

2016 Fiscal Year Final Research Report

• Project/Area Number: 26540016
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• 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(Renkei-kenkyūsha): MATSUE Kaname 九州大学, マス・フォア・インダストリ研究所, 助教 (70610046)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 多変量解析 / 代数的位相幾何 / 多様体学習

Outline of Final Research Achievements

(1) Kernel methods for vectorizing persitence diagrams has been proposed, and they have been applied to detecting the phase transition temperature between glass and liquid. (2) A framework for phyogeny analysis has been proposed based on manifold learning and gene clustering. (3) The method of Euler number has been applied to derive reliability intervals of regression problems as well as the distribution of maximum eigenvalue of random matrices.

Free Research Field

統計的機械学習