2005 Fiscal Year Final Research Report Summary
Nonlinear Data Analysis for Functional Data
| Project/Area Number |
14380122
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
MIZUTA Masahiro Hokkaido Univ., Information Initiative Center, Prof., 情報基盤センター, 教授 (70174026)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Yoshiharu Hokkaido Univ., Grad.School of Info.Sci., Prof., 大学院・情報科学研究科, 教授 (80091461)
MURAI Tetuya Hokkaido Univ., Grad.School of Info.Sci., Asso.Prof., 大学院・情報科学研究科, 助教授 (90201805)
SUZUKAWA Akio Hokkaido Univ., Grad. School of Eco., Asso.Prof., 大学院・経済学研究科, 助教授 (00277287)
MINAMI Hiroyuki Hokkaido Univ., Information Initiative Center, Asso.Prof., 情報基盤センター, 助教授 (80261395)
KOMIYA Yuriko Hokkaido Univ., Information Initiative Center, Inst., 情報基盤センター, 助手 (40241393)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Functional Data / Functional Regression Analysis / Functional MDS / Functional Clustering / Discrete Functional Data / Difference / Difference Equation / Dimension Reduction |
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| Research Abstract |
In most conventional data analysis methods, we assume that data set is regarded as a set of numbers with some structures, for example a set of vectors or a set of matrices etc. Nowadays, we must often analyze more complex data. One type of the complex data is functional data structure ; data themselves are represented as functions. Ramsay and Silverman have studied function data analysis (FDA) as the analysis method to function data since the 1990's. They have published excellent books on FDA (Ramsay & Silverman, 1997, 2002).
In this study, we promoted the research of the function data analysis method, the building of a theory system, an application study to the practical problems and so on.
Specifically, we discussed with Prof. Ramsay and the experts of the statistical science and the information engineering. Based on those discussions, we reviewed about the expansion of the coverage of FDA. Moreover, by using the knowledge of the nonlinear data analysis, the new analysis methods were developed.
Study results are classified into the following.
(1)The definition of the framework of the function data :
We investigated a research trend about the function data analysis. We reviewed the directionality of this research task.
(2)Developments of methods for Functional Data Analysis :
We developed methods for FDA including functional regression, functional MDS and functional clustering.
(3)Discrete functional data analysis :
We proposed a method to find the structures that the discrete functional data have by utilizing the proposed high order differences.
(4)The research of the related field :
We dealt with virtual parallel computer environment, dimension reduction methods and variable selection as the related topics.
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