摘要
为了完善轮廓相似性度量的概念和计算,拓展轮廓相似度计算公式的应用,讨论了样本几何轮廓的序结构和表示定理,修正了轮廓相似性的度量公理与计算公式.在样本几何轮廓和"轮廓优"序的定义下,证明了"轮廓优"序的"严格弱序"结构,证明了在轮廓相似性分析问题中表示定理成立,奠定了约定"轮廓相似性度量公理"的逻辑基础,进而定义了样本几何轮廓的"相似度"序,证明了"相似度"序的"严格偏序"结构,并修正了轮廓相似度计算公式.使轮廓相似分析的概念与相似度计算公式能适应不同背景下的多标度数据分析的要求.
In order to improve the concept and calculation of the measurement of outline similarity and widen the application of the outline similarity calculation formulae,this paper will discuss the sequence structure and representation theorem of sample geometric profile and adjust the measure axiom and calculation formulae of outline similarity.Under the definition of the sample geometric profile and the 'contour superior'sequence,this study proves the 'strictly weak sequence' structure of 'profile optimal' sequence and the representation theorem in the outline similarity analysis,which establish the logical basis for the measure axiom of outline similarity.Based on the study results,this study also defines the 'similar degree' sequence of sample geometry outline,and proves the 'strictly partial order' structure of 'similarity' sequence and revises the outline similarity calculation formulae.This study makes the concept of outline similarity analysis and similarity calculation formulae to be able to adapt to the requirements of multi-scale data analysis in different backgrounds.
出处
《辽宁工程技术大学学报（自然科学版）》
CAS
北大核心
2012年第5期797-800,共4页
Journal of Liaoning Technical University (Natural Science)
基金
教育部高校博士学科点专项科研基金资助项目(20102121110002)
关键词
多标度数据
几何轮廓
序结构
相似性度量公理
址联系数
标联系数
轮廓相似系数
轮廓相似度
multi-scale data
geometric profile
sequence structure
similarity measure axiom
address correlation coefficient
scale correlation coefficient
outline similarity coefficient
outline similarity
