An article to take you through the principal component analysis in mathematical modeling (the sample application explanation of water quality problems in 2005 includes code)

1. Understanding of principal component analysis

Principal Component Analysis (PCA) is a statistical method. In dealing with practical problems, there may be a certain correlation between multiple variables. When there are a large number of variables and there are complex relationships between variables, it increases the difficulty of problem analysis. Principal component analysis is a mathematical method of dimensionality reduction. This method mainly recombines a large number of previously correlated variables into a new kind of unrelated comprehensive variables.

2. Topic analysis

Make a quantitative comprehensive assessment of the water quality of the Yangtze River in the past two years, and analyze the water pollution in various regions

Taking into account that there may be a certain correlation between the indicators, the principal component analysis method is used to analyze the water quality inspection reports of the major cities in the Yangtze River Basin, and the principal components are selected and theThe main component scores are weighted and summed according to the variance contribution rate to obtain the comprehensive pollution evaluation index of each area, and then the comprehensive pollution evaluation index of the Yangtze River basin can be calculated every month, and the average comprehensive evaluation index can be sorted

Three, principle formula

According to the method of principal component analysis, the detection data of four main water quality indicators from 17 observation stations along the Yangtze River were analyzed in the past two years.
Proceed as follows: