Component Analysis Model of Glass Relics Based on Logistic Regression and Fisher Linear Discrimination

Abstract

In recent years, with the attention paid by various countries to the exploitation and protection of cultural relics and the continuous development of industrialization, people have gradually realized the necessity of analyzing the weathering of ancient glass relics. In this paper, the physical characteristics, chemical composition and content of sample cultural relics are analyzed and their types are identified by using multiple algorithms such as Logistic regression model, Fisher linear discrimination, Fisher’s exact test, etc. The study of this issue can provide guiding suggestions for the analysis and classification of ancient cultural materials, and help archaeologists carry out a series of work such as cultural relics protection. The results show that the "type" factor has the greatest relationship with weathering, followed by "color" and "decoration". The regression equation between the sample and weathering chemical composition is established, and it is concluded that "type" and "SnO₂" have a large negative correlation with weathering, "MgO" and "SO₂" have a large positive correlation, and other variables have a weak correlation. Finally, Fisher linear discriminant method is used to identify the category of unknown glass relics. By estimating the training group and testing the test group, it is found that the algorithm can correctly classify 100.0% of the original grouped cases. We can identify the unknown cultural relics and find that A1, A5, A6 and A7 cultural relics belong to high potassium glass, and the rest belong to lead barium glass. In order to test the accuracy of the model in identifying the category of glass relics, Fisher's exact test algorithm was used. It was found that the classification results were more sensitive to silica in the fluctuation range of - 50% to - 25%, and less sensitive to other chemical components, it is stable.