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基于特征点分布的多元灰色绝对关联度

ISSN号：1001-506X
期刊名称：《系统工程与电子技术》
时间：0
分类：N941.5[自然科学总论—系统科学]
作者机构：[1]河海大学商学院,中国南京211100, [2]南京工程学院车辆工程系,中国南京211167
相关基金：国家自然科学基金（71101043,70901041,71171113）资助项目;国家社会科学基金（10ZD＆014,11＆ZD168）资助项目;国家自然科学基金与英国皇家学会合作交流基金（71111130211）资助项目;教育部博士点基金（20093218120032,200802870020）资助项目;江苏省青蓝工程青年杰出教师基金资助项目;南京航空航天大学科研业务基金（NR2011002）资助项目;河海大学中央高校科研业务基金（2011809914,2010B11114）资助项目.

关键词：灰色系统, 绝对灰色关联度, 多元时间序列, 相似性度量, grey system, absolute degree of grey incidences , multivariate time series, similarity measure

中文摘要：

针对多元灰色绝对关联度存在分析结果与定性判断相矛盾的问题，探讨一种基于点分布特征的灰色绝对关联分析模型。该模型依据多元序列的几何描述，分区域提取邻域极值，构造多元序列的特征点集；然后根据特征点的分布特性获取反映多元序列几何特征的特征点序列；将多元序列的关联分析转化为特征点序列问的相关性分析，从而建立关联度模型。该模型具有平移不变性、转置和行列变换不变性、满足灰色关联分析公理要求。最后，通过两个实例验证了该模型的有效性。

英文摘要：

The analysis result of absolute degree of grey incidence for multivariate time series is often inconsistent with the qualitative analysis. To overcome this shortage, a multivariate absolute degree of grey incidence based on distribution characteristics of points is proposed. Based on the geometric description of multivariate time se- ries, the neighborhood extrema are extracted in the different regions, and a characteristic point set is constructed. Then according to the distribution of the characteristic point set, a characteristic point sequence reflecting the ge- ometric features of multivariate time series is obtained. The incidence analysis between multivariate time series is transformed into the relational analysis between characteristic point sequences, and a grey incidence model is established. The model possesses the properties of translational invariance, transpose and rank transform invari- ance, and satisfies the grey incidence analysis axioms. Finally, two cases are studied and the results prove the ef- fectiveness of the model.