| Hu Chunyan,Hu Liangping,Reasonably carry out multivariate analysis： generalized principal component analysis[J].SICHUAN MENTAL HEALTH,2023,36(S1):55-60 |
| Reasonably carry out multivariate analysis： generalized principal component analysis |
DOI：10.11886/scjsws20230605002 |
| English keywords:Synthetic data Logarithmic centralization Covariance matrix Sample sorting Generalized principal component |
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| The purpose of this paper was to introduce the basic concepts， calculation methods， two examples and SAS implementation related to generalized principal component analysis. Basic concepts included synthetic data， quasi-synthetic data， partial synthetic data and generalized principal component analysis. The calculation method involved logarithmic centralization， constructing the covariance matrix S and finding the eigenvalues and eigenvectors of the matrix S. The data involved in the two examples were percentage content of 5 components in a certain ore and household consumption data of farmers in 30 regions of China in 1993.With the help of SAS software， generalized principal component analysis was carried out on the quantitative data in the two examples. Only one principal component was needed to contain more than 85% of the information contained in multiple original variables， and a good dimensionality reduction effect had been achieved. In example 2， based on the calculation results of generalized principal components， the sorting and preliminary classification of regions were also realized. |
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