Analysis and Identification of Glass Composition Based on Logistic Regression and PCA+k-means Clustering

This paper analyzes the data of question C of the “Higher Education Society Cup” National Undergraduate Mathematical Modeling Contest in 2022, analyzes and identifies the components in glass relics. Firstly, Eliminating Fixed Sum Constraints of Various Components in Glass through Central Log-Ratio Transformation, and the change amount and rate of chemical composition of high-potassium and lead-barium glasses before and after weathering were preliminarily explored, and the data were analyzed by chi-square and corrected chi-square. Then, the composition of different glass types was analyzed by binary Logistic regression model. Finally, the PCA+K-Means coupling model is established to classify the high-potassium glasses. It is found that the change amount and change rate of each component of different types of glass are different before and after weathering, and the distribution is also different. That is to say, different types of glass have significant effects on the surface weathering of glass, but the effects of glass decoration, color and weathering are not significant. And different chemical substances have a significant impact on the classification of ancient glass products. At the same time, the subcategories of high-potassium glasses can be divided into four categories according to the contents of calcium oxide, magnesium oxide and alumina.