GLOBAL CORRELATION METHODS FOR FEATURING A RANDOM FIELD AND A MULTIDIMENSIONAL MULTIVARIATE TIME SERIES AND THEIR APPLICATIONS

随机场和多维多元时间序列的全局相关方法及其应用

• 批准号: 08680336
• 负责人: KIKKAWA Sho
• 金额: $ 1.54万
• 依托单位: KINKI UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08680336/
• 关键词: RANDOM FIELD; NUMBER OF DEGREES OF FREEDOM; CORRELATION TIME; CORRELATION LENGTH; CORRELATION AREA; BUNDLE CORRELATION FUNCTION; METEOROLOGICAL DATA; BIOMEDICAL DATA; 大域的相関; 統計的自由度; 相互情報量; 多次元多変量時系列; 相関体積; 面相関関数; 線相関関数; 面相関時間; 束相関関数; 束相関時

(a)We defined statistical numbers of degrees of freedom (NDF) as an equivalent uncorrelated number of points per unit area in a 2-dimensional random field.(b)The first order NDF is equal to Fisher's information about the first statistical moment. The second order NDF is an approximation of Fisher's information about the second moment.(c)Many interesting features of a random field and a random process were deduced from the NDF's. They are correlation time, correlation length, correlation area, line-correlation, area-correlation, and bundle-correlation.(d)The mutual information and the vector correlation coefficient between two random processes are useful to measure how they are globally correlated. Relationship between mutual information and vector correlation were investigated both theoretically and numerically.(e)The results obtalned above were applied to annualizing some meteorological data and biomedical data.

（a）我们将自由度（NDF）的统计数定义为在二维随机场中每单位区域的等效点数。第二阶NDF是Fisher关于第二刻的信息的近似。（c）从NDF中推导了随机字段和随机过程的许多有趣特征。它们是相关时间，相关长度，相关面积，线相关，区域相关和束相关。（d）两个随机过程之间的相互信息和矢量相关系数对于测量它们的全球相关性很有用。在理论上和数值上都研究了相互信息与矢量相关性之间的关系。（e）上述结果用于年度化某些气象数据和生物医学数据。

项目成果

Kikkawa, Sho: "A global correlation method and its application to analysis of multivariate metereological data" 1994-1996 Report of Research Project, Grant-in-Aid-for Scientific Research (A) (1), (Project number 06301031) (Togo, M.). (1997)

Kikkawa, Sho：“全球相关方法及其在多元气象数据分析中的应用”1994-1996 年研究项目报告，科学研究资助 (A) (1)，（项目号 06301031）（多哥）

Kikkawa, Sho: "Prospects of the theory of time-frequency analysis I-An introduction to nonstationary spectra-" The Journal of the Institute of Electronics, Information and Communication Engineers. B-79 (5). 515-520 (1996)

Kikkawa，Sho：“时频分析理论的展望I-非平稳谱简介-”电子信息与通信工程师学会杂志。

Kikkawa, Sho: "Prospects of the theory of time-frequency analysis V-Cohen's class-" The Journal of the Institute of Electronics, Information and Communication Engineers. B-79 (9). 927-935 (1996)

Kikkawa，Sho：“时频分析理论的展望V-Cohen的课-”电子信息通信工程师学会杂志。

吉川 昭: "時間-周波数解析の展望II-マッチドフィルタから非定常スペクトルへ-" 電子情報通信学会誌. B-79(6). 597-602 (1996)

Akira Yoshikawa：“时频分析的观点 II - 从匹配滤波器到非稳态频谱 -”电子、信息和通信工程师学会杂志 B-79(6) (1996)。

太田喜元、東本暁美、吉川 昭、: "生物工学概論" コロナ社, 279 (1998)

Yoshimoto Ota、Akemi Higashimoto、Akira Yoshikawa：《生物工程导论》Coronasha，279 (1998)