Identification of the Origin of Emerald Based on SPSS Factor Analysis and Discriminant Analysis

The geographic origin tracing of gemstones has always been an important topic of concern in jewelry industry. The origin of gems is closely related to price, and the development of computer and artificial intelligence makes it possible to use mathematical models in this field. In order to study the origin determination methods of the same kind of gemstones from different areas and eliminate the subjectivity, empiricism and uncontrollability of traditional origin determination methods, this study used the chemical composition data of emerald from different areas summarized by self-test and predecessors. Factor analysis and discriminant analysis were combined with SPSS to discriminate the origin of 242 emerald samples from nine different areas such as Zambia, Australia, Colombia, Madagascar, Pakistan etc. The experimental variables are the content of Li, Na, K, Rb, Cs, Sc and the Ga and the results show that: (1) Multicollinearity analysis of factor analysis and linear regression can be obtained, there is no obvious multicollinearity between these seven groups of element variables, and the KMO value of factor analysis is slightly less than 0.6, that is, the correlation between them is not obvious; (2) Discriminant analysis shows that the correct rate of back generation to distinguish the origin of emeralds from the nine producing areas by using these element contents is 95.9%, the correct rate of cross-validation is 91.7%, and the discriminant model has a high correct rate of discrimination and it has a good degree of discrimination. Therefore, it has great potential to use the alkali metal chemical elements in emeralds from different origins as variables to establish a discriminant model to trace their origins.