Multivariate statistical analysis Chapter V principal component analysis - 01

5.1 The basic principle of principal component analysis

In multivariate statistics, too many variables need to be considered to avoid missing important information , The increase of these excessive variables greatly increases the complexity of the problem . Because each index reflects the same thing , Inevitably, a large amount of information overlap . therefore , People want fewer variables in quantitative research , Get more information . Principal component analysis is to study the linear combination of the original variables to explain the original variables most A multivariate statistical method of information

Geometric meaning

Take two dimensions

among X1 And X2 It's the original variable , Through the following linear combination Y1 and Y2 It can be seen that the points in this example are represented by Y1 and Y2 Is in the standard ellipse under the coordinate axis

summary

The process of principal component analysis is nothing more than the process of coordinate system rotation , Each principal component expression is the transformation relationship between the new coordinate system and the original coordinate system , In the new coordinate system , The direction of the coordinate axis is the direction in which the original data changes the most （ I don't understand this sentence ）