Application Of Principal Component Analysis And Factor Analysis Based On Mathematical Models

Principal component analysis and factor analysis are two important and useful multivariate statistical methods, in this article, from the theoretical and applied aspects of the principal component analysis and factor analysis carried out studies. The article on the principle of the principal component analysis and mathematical derivation nature proves, and discusses the mechanism of principal component analysis and improvement methods. This paper made a further study of the factor analysis estimation methods and specific factor loading matrix factor variance for a more comprehensive evaluation objectively and accurately made theoretical preparation. In terms of concept, basic ideas, mathematical model, calculation compared the similarities and differences between the two methods. In the comparative study of the similarities and differences between the two on the basis of practical application showed that the two methods in the application process problems should pay attention to the problem, especially in the implementation process of the SPSS statistical software should pay attention to. By contrast with the conventional weighted average method, verify the feasibility of the two methods in scientific and comprehensive evaluation of applications. Based on the characteristics of the two methods, summed up the choice of which method is more appropriate in different circumstances.The principal component analysis and factor analysis which is proposed in this paper are done by the SPSS statistical software,and this paper has thirty-three students’ grades as an example.The superiority of these methods are proved by the calculating results. The results are satisfactory.