Nonlinear Data Analysis for Functional Data

函数数据的非线性数据分析

• 批准号: 14380122
• 负责人: MIZUTA Masahiro
• 金额: $ 8.26万
• 依托单位: HOKKAIDO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14380122/
• 关键词: Functional Data; Functional Regression Analysis; Functional MDS; Functional Clustering; Discrete Functional Data; Difference; Difference Equation; Dimension Reduction; 放射線医療; 関数解析; 主成分分析; 時系列データ; 高速計算; 最適化問題; 計算機指向手法; 関数非類似度データ

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.

在大多数传统的数据分析方法中，我们认为数据集是一组具有一定结构的数字，例如一组向量或一组矩阵等。如今，我们必须经常分析更复杂的数据。一类复杂数据是功能数据结构；数据本身被表示为函数。Ramsay和Silverman从20世纪90年代开始研究功能数据分析（FDA）作为功能数据的分析方法。他们出版了关于FDA的优秀书籍（Ramsay & Silverman, 1997,2002）。在本研究中，我们推进了函数数据分析方法的研究、理论体系的构建、对实际问题的应用研究等。具体来说，我们与Ramsay教授以及统计科学和信息工程方面的专家进行了讨论。在这些讨论的基础上，我们回顾了FDA覆盖面的扩大。利用非线性数据分析的知识，提出了新的分析方法。研究结果分为以下几类。(1)函数数据框架的定义：探讨了函数数据分析的研究趋势。我们回顾了本研究任务的方向性。(2)功能数据分析方法的发展：我们开发了包括功能回归、功能MDS和功能聚类在内的FDA方法。(3)离散泛函数据分析：我们提出了一种利用所提出的高阶差分来发现离散泛函数据结构的方法。(4)相关领域的研究：研究了虚拟并行计算机环境、降维方法和变量选择等相关问题。

项目成果

Possibilities and Problems of the XML-based Graphics in Statistics

统计中基于 XML 的图形的可能性和问题

• 发表时间: 2004
• 期刊: COMPSTAT2004, Proceedings in Computational Statistics
• 作者: T.Fujino;Y.Yamamoto;T.Tarumi
• 通讯作者: T.Tarumi

Functional Data and Functional Data Analysis

功能数据和功能数据分析

• 发表时间: 2005
• 期刊: Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 17(4)
• 作者: M.Mizuta;T.Shimamura;水田正弘;M.Mizuta;T.Shimamura;M.Mizuta
• 通讯作者: M.Mizuta

Multidimensional scaling for dissimilarity functions with continuous argument

具有连续参数的相异函数的多维标度

• 发表时间: 2003
• 期刊: Journal of the Japanese Society of Computational Statistics 15(2)
• 作者: 弘 新太郎;小宮由里子;南 弘征;水田正弘;M.Mizuta;H.Minami;T.Tokairin;佐藤義治;水田正弘;山本義郎;M.Mizuta;M.Mizuta;M.Mizuta
• 通讯作者: M.Mizuta

Dimension Reduction Methods

• DOI: 10.1007/978-3-642-21551-3_22
• 发表时间: 2012
• 作者: M. Mizuta

Modelling 3D Respiratory Tumor Motion with Markov-Switching Vector Autoregressive Process Vector Autoregressive Process

使用马尔可夫切换向量自回归过程建模 3D 呼吸肿瘤运动 向量自回归过程

• 发表时间: 2005
• 期刊: Bulletin of the International Statistical Institute 55
• 作者: Teppei Shimamura;Hiroki Shirato;Masahiro Mizuta
• 通讯作者: Masahiro Mizuta