Fisher Linear Discriminant and Systematic Cluster Analysis based on analysis and identification of the composition of ancient glass products

Abstract

The Silk Road was a channel of cultural exchange between China and the West in ancient times, of which glass was a valuable physical evidence of early trade exchanges. Therefore, it is important to analyze the ancient glass products for the research related to ancient times. In this paper, in order to get the classification law of high potassium and lead-barium glass, firstly, the discriminant relationship function was obtained by using Fisher Linear Discriminant Analysis. Secondly, the data were downscaled by Principal Component Analysis to get five principal components, and then Fisher Linear Discriminant Analysis was used to get the discriminant function, and the results all passed the cross-check, and the model accuracy was 95.29% and 91.43%, respectively. The subclasses were classified by Systematic Clustering Model and Elbow Method, and it was concluded that the high potassium glass was mainly divided into two subclasses based on whether the silica content was greater than 80%; the lead-barium glass was mainly divided into four subclasses based on the content of three different chemical components: silica, barium oxide and phosphorus pentoxide. And through the reasonableness and sensitivity analysis, this paper got that different chemical compositions have different size influence on the classification of glass.