基于CLR的玻璃文物成分分析与分类模型  

Classification Model for Glass Relics Based on Compositional Data Analysis through CLR Transformation

作　　者：邓天宇 邱奕珲 池正昊 DENG Tianyu;QIU Yihui;CHI Zhenghao(School of Management,Fudan University,Shanghai 200433,China)

机构地区：[1]复旦大学管理学院,上海200433

出　　处：《数学建模及其应用》2023年第2期41-51,共11页Mathematical Modeling and Its Applications

摘　　要：对具有成分数据特征的古代玻璃成分数据集进行风化前成分含量预测以及类别划分.首先,对成分数据进行中心对数比变换预处理,从“成分相对重要性”的角度提取了成分数据的信息,并通过对变换后的玻璃文物化学成分数据分析:一方面,实现了对已风化的铅钡和高钾两类玻璃风化前化学成分的预测,即成分还原;另一方面,在铅钡和高钾两大类的基础上,拣选出可用于对玻璃文物进一步分出亚类的化学成分,构建了稳健的玻璃亚类分类模型.该模型可以实现在风化导致玻璃文物偏移其原始化学成分的情况下,对玻璃的亚类有大致正确的判断,即对风化文物原始成分的预测偏差不会显著影响分类结果.We first apply centered log-ratio transformation on given compositional dataset of glass relics to capture information of "relative importance of a specific composition".After analysis on the transformed compositional data,we′ve achieved two main purposes.First,we can predict the pre-weathering composition of a glass relic using its known post-weathering composition.We call it as composition restoration.Second,selecting out reasonable criteria,we work out a robust subclass classification model for glass relics,which can accurately recognize the subclass of a weathered relic regardless of prediction bias caused by composition restoration.Our work is practically essential for archaeologists in face of weathered glass relics.

关 键 词：风化 玻璃文物 成分还原 中心对数比变换 层次聚类 文物亚类划分 

分 类 号：O29[理学—应用数学]