基于成分数据的古代玻璃制品分析与分类  

Analysis and Classification of Ancient Glass Products Based on Compositional Data

作　　者：马佩莹 韩雁来 李德兰 陈佳佳 MA Peiying;HAN Yanlai;LI Delan;CHEN Jiajia(School of Statistics,Shanxi University of Finance and Economics,Taiyuan,Shanxi 030006,China)

机构地区：[1]山西财经大学统计学院,山西太原030006

出　　处：《数学建模及其应用》2023年第2期63-73,共11页Mathematical Modeling and Its Applications

基　　金：山西省高等学校教学改革创新项目(J20220570)。

摘　　要：古代玻璃制品的化学成分属于成分数据,基于成分数据分析方法可以对玻璃制品的化学成分进行分析,研究其分类规律,并对未知玻璃文物鉴别其所属类型.首先,基于Spearman相关系数以及卡方检验分析玻璃文物表面风化与其类型、纹饰、颜色的关系;通过单形空间均值来分析玻璃表面有无风化化学成分含量的统计规律;构建Dirichlet回归模型来预测风化点风化前的化学成分含量.其次,构建决策树、偏最小二乘判别分析两种模型对两类玻璃进行初分类特征选择;进一步,用K-means聚类对两类玻璃进行亚分类,并通过偏最小二乘判别分析对两类玻璃进行亚分类特征选择;进而,利用所得分类规律对未知类别玻璃鉴别其所属类型.最后,运用灰色关联分析分别探究两类玻璃化学成分之间的关联关系及其差异性.The chemical composition of ancient glass products belongs to the compositional data.Therefore,using the compositional data analysis method,the chemical composition of glass products is analyzed and its classification rule is studied,thus the type of unknown glass relics is identified.Firstly,based on Spearman correlation coefficient and Chi-square test,the relationship between surface weathering of glass relics and its type,decoration and color were analyzed;the statistical rule of weathering chemical composition on glass surface was analyzed by means in simplex space;the Dirichlet regression model was constructed to predict the chemical composition before weathering.Secondly,two models of decision tree and partial least squares discriminant analysis were constructed to select the features of the initial classification of the two types of glass;further,K-means clustering was used to sub-classify the two types of glass,and partial least squares discriminant analysis was used to sub-classify the two types of glass;then,the classification rules were used to identify the unknown type of glass.Finally,grey correlation analysis was used to explore the correlation and difference between the two types of glass chemical components.

关 键 词：成分数据 决策树 偏最小二乘判别分析 K-MEANS聚类 灰色关联 

分 类 号：O29[理学—应用数学]