矩阵灰色绝对关联度及其意义  

Matrix absolute grey relation degree and its significance

作　　者：王双维[1] 张莎[1] 赵利民 李雅丹[1] 曹晓琳[3] 

机构地区：[1]东北师范大学物理学院,吉林长春130024 [2]长春市环境监测中心站,吉林长春130022 [3]吉林大学汽车工程学院,吉林长春130025

出　　处：《东北师大学报（自然科学版）》2009年第4期73-78,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(50478007);吉林省环保局科技项目(2008-23)

摘　　要：首次提出了矩阵灰色绝对关联度的概念,并对相应性质进行了数学证明,给出了曲面灰色关联分析的实例验证.已有灰色关联理论只能进行序列之间的关联分析,其几何意义是曲线之间的整体相似性比较;给出的矩阵灰色绝对关联度可以进行相同维度矩阵之间的关联分析,其几何意义是曲面之间的整体相似性比较.矩阵灰色关联分析有望为诸如环境监测点位优化、图像处理中的人脸部位提取等二维信号处理提供新的技术手段.Absolute grey relation degree of matrix is proposed as a new concept in this paper. Moreover mathematical justification and surface verification cases using this theory are given. Available grey relation degree theory is limited in using in sequence relation analysis to reveal and compare comparabilily of whole curves. The theory presented in this discourse can be used in relation analysis of equal dimension matrixes. Its geometric meaning is expanded to comparability comparison of whole surfaces. This theory can be used as a new technical approach for two dimensional signal processing such as en vironmental monitoring site optimization and feature extraction in human face.

关 键 词：灰色系统 矩阵灰色绝对关联度 矩阵灰色关联分析 图像处理 

分 类 号：N941.5[自然科学总论—系统科学]