Nonlinear Data Analysis with Algebraic Curve Fitting

使用代数曲线拟合的非线性数据分析

• 批准号: 09480048
• 负责人: MIZUTA Masahiro
• 金额: $ 7.55万
• 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: 1997
• 资助国家: 日本
• 起止时间: 1997 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-09480048/
• 关键词: Implicit Function; Multivariate Data Analysis; Data Mining; Latent Structure; Curve Fitting; Sliced Inverse Regression Analysis; Principal Points; Generalized Principal Components Analysis

The aim of the research is to construct a series of methods for nonlinear data analysis. Data analysis methods with algebraic curve fitting are fundamental methods in the research. We had studied algebraic curve fitting at first. We developed an algorithm to derive the exact distance between a point and algebraic curve. A method for finding an algebraic curve structures in data is proposed. According to the progress of the research, we also study Generalized Principal Components Analysis and Principal Curves. For related data analysis methods, Sliced Inverse Regression, Functional Data Analysis and Principal Points are studied. Sliced Inverse Regression with Projection Pursuit is proposed and numerical examples show the advantages of the proposed method. A method of nonlinear functional regression analysis is developed.

本研究的目的是构建一系列的非线性数据分析方法。采用代数曲线拟合的数据分析方法是本研究的基本方法。我们首先研究了代数曲线拟合。我们开发了一种算法来求出点和代数曲线之间的精确距离。提出了一种在数据中寻找代数曲线结构的方法。根据研究进展，本文还对广义主成分分析和主曲线进行了研究。对于相关的数据分析方法，主要研究了分片逆回归、函数数据分析和主点法。提出了投影寻踪的分层逆回归方法，数值算例表明了该方法的优越性。提出了一种非线性函数回归分析方法。

项目成果

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Akira Tanaka、Hideyuki Imai、Masaaki Miyakoshi：“使用二次不等式约束的投影滤波器进行图像恢复”IEICE Transactions D-II，3. 415-421 (1999)

Y.Sato: "An Autonomous Clustering Technique."Data Analysis, Classification and Related Methods, Springer. 23-28 (2000)

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Y.Kudo, T.Murai, and T.Da-te: "A Possibilistic Interpretation of Extended Erasure."Proceedings of the Fifth European Congress on Intelligent Techniques and Soft Computing. 77-80 (1997)

Y.Kudo、T.Murai 和 T.Da-te：“扩展擦除的可能性解释”。第五届欧洲智能技术和软计算大会记录。

M.Kawane, Y.Komiya, and M.Mizuta: "Cluster Analysis with Parallel Virtual Machine."Proceedings of the Tenth Japan and Korea Joint Conference of Statistics. 101-106 (2000)

M.Kawane、Y.Komiya 和 M.Mizuta：“并行虚拟机的集群分析”。第十届日本和韩国统计联合会议论文集。

M.Kudo, H.Imai, T.Murai, and M.Shimbo: "An MDL-Based Classifier for Multidimensional Space."Proceeding of the Fourth World Multiconference on Systemics, Cybernetics, and Informatics. 498-503 (2000)

M.Kudo、H.Imai、T.Murai 和 M.Shimbo：“基于 MDL 的多维空间分类器”。第四届世界系统学、控制论和信息学多重会议论文集。