古代玻璃制品成分分析与鉴别的统计建模  

Statistical Modeling and Analysis of Ancient Glass Composition

作　　者：宛惠 邓明华[1] WAN Hui;DENG Minghua(School of Mathematical Sciences,Peking University,Beijing 100871)

机构地区：[1]北京大学数学科学学院,北京100871

出　　处：《数学建模及其应用》2023年第2期27-40,共14页Mathematical Modeling and Its Applications

基　　金：国家自然科学基金(31871342)。

摘　　要：给出2022年“高教社杯”全国大学生数学建模竞赛C题“古代玻璃制品的成分分析与鉴别”可行的解法,并对赛题评阅进行简要评述.该题旨在通过对古代玻璃制品的化学成分数据分析,探索文物分类方法.本文在充分考虑数据的成分性特点基础上,采用中心对数比变换将数据从单纯型映射到欧式空间,在变换后的空间上进行相应的统计分析.This paper presents a feasible solution to problem C"Ancient glass composition analysis and discrimination"in 2022 Higher Education Press Cup China Undergraduate Mathematical Contest(CUMCM 2022),and gives a brief summary of review process.The aim of this problem is analyzing the chemical composition and exploring classification method for ancient glasses.The most important characteristics of this problem is its compositional data.Considering the compositional characteristic of the data,we use the central log-ratio transformation,which transform the compositional data in simplex space to Euclidean space,then the corresponding statistical analysis can be done in Euclidean space.

关 键 词：成分数据 中心对数比变换 有监督分类 无监督聚类 关联分析 

分 类 号：O29[理学—应用数学]