# K-Means++ Clustering Algorithm in Categorization of Glass Cultural Relics
## 1 Introduction  
Glass has long been recorded among Chinese historical materials, but research on ancient Chinese glass started late. There is a lack of research on the weathering and composition of ancient silicate glass, and most of it is from the perspective of dynasty replacement. The cultural and artistic forms of glass and the laws of its own operation and development are studied in terms of cultural exchange and chemical analysis. Few scholars have systematically established mathematical models and used intelligent algorithms to qualitatively and quantitatively predict the original composition and subclassification methods of weathered silicate glass.  
Machine-learning algorithms play an important role in the exploration of ancient cultures nowadays, helping in the search for statistical insight and classification. Data measurements and statistical analyses of the chemical compositions of ancient cultural relics, looking for statistical rules and classifying the types of cultural relics, can provide a reliable basis for identifying the types of ancient cultural relics and tracing the history of ancient cultural relics from a statistical perspective. In the most basic way, ancient glass cultural relics discovered in China are mainly divided into two categories: high-potassium and lead-barium glass. This is because in the process of making these glasses, people needed to add many kinds of auxiliary solvents into the main part, SiO\({}_{2}\). Commonly seen in the southeast of China, the high-potassium glass usually has plant ash as its auxiliary solvent, which is rich in potassium (in the form of K\({}_{2}\)O), while the lead-barium glass is located elsewhere in China, rich in PbO and BaO [1,2]. As time went by, some of the glass relics were weathered and their chemical compositions changed accordingly. [PERSON]'s [3]in-depth study on the mechanism of weathering has certain reference significance for component prediction. [PERSON], et al. [4] classified the chemical composition of glassware by nondestructive analysis of pXRF. However, the existing chemical research methods cannot accurately and reasonably classify according to the composition of glass. Therefore, we consider introducing machine learning to solve practical problems by using classification models and intelligent algorithms. Intelligent algorithms have been widely used in scientific research in the field of materials in recent years, such as for the construction and application of the database of ancient Chinese unearthed glass beads studied by [PERSON] [5] and the summary by [PERSON] [6] of the main theoretical basis, simulation process, and application status of each simulation method by using seven simulation methods of glass composition properties, but there are few methods that shed light on the specific field of glass relics. [PERSON] [7] conducted glass defect detection based on deep learning, but there is still a gap in the use of machine learning to study the weathering and subclassification of ancient glass at home and abroad [8].  
In this paper, we first study the classification rules of high-potassium glass and lead-barium glass by statistical methods and try to recover the original proportion of chemical elements of weathered points, i.e., their chemical composition before being weathered, by statistical methods. After that, we conduct the subcategorization based on dimensionality reduction by PCA and make an evaluation. The K-Means++ clustering model is established using three principal components, and the rationality and sensitivity of the model are tested.  
The rest of this paper is organized as follows: In Section 2, the classification law of high-potassium glass and lead-barium glass are studied based on sample data. Section 3 proposes the K-Means++ clustering algorithm and establishes the classification model. In Section 4, the validity of the model is analyzed. Section 5 analyzes the model sensitivity. Section 6 discusses limitations of the study and future work. The conclusions are provided in Section 7.