In response to question 1, the key lies in the need to study the relationship between weathering and type, ornamentation and color on the surface of glass products, as well as the relationship and law between each glass type and chemical composition content. By establishing decision trees, chi-square tests, and multiple linear regression models, after eliminating two sets of invalid data from samples 15 and 17, it was concluded that the type and ornamentation of glass products have a greater influence on weathering, and the color of glass products has a smaller relationship with weathering The relationship between glass type and weathering is smaller, and the variation of chemical composition content with and without weathering is more obvious for different glass types, and the statistical pattern of these data is used to predict the chemical composition content of each glass type before weathering. For problem 2, different categories of glass need to be subclassified according to chemical composition. By establishing a decision tree model, the classification rules of glass types were found out, such as lead oxide content higher than 5.46 for lead-barium glass and lower than 5.46 for high-potassium glass, and the entropy weighting method was used to determine the weights of various chemical components for high-potassium glass with or without weathering and lead-barium glass with or without weathering, so that the chemical components with higher weights were selected to classify four types of glass: high-potassium weathered, high-potassium unweathered, lead-barium weathered, and lead-barium unweathered, respectively. The classification results were obtained by using the systematic hierarchical clustering algorithm, and the classification results of different types of glass differed, and then the results were analyzed for reasonableness and sensitivity.

Sha Yuan. A model for compositional analysis of ancient glass products based on correlation analysis. Academic Journal of Mathematical Sciences (2022) Vol. 3, Issue 2: 63-68. https://doi.org/10.25236/AJMS.2022.030210.

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