GPS Principal Component Analysis

　　The main purpose of principal component analysis [6] is to replace the original multi-dimensional variables with a few comprehensive variables after linear transformation and discarding part of the information on the premise of ensuring the minimum information loss of the original data. Among all extracted principal components, the first principal component contains the most variable information that can be explained, the second principal component contains the second most variable information that can be explained, and the last principal component contains the least variable information.

　　The main steps of principal component analysis are:

　　1) Calculate the eigenvalues and eigenvectors of the X autocorrelation matrix according to the original data X;

　　2) Sort the eigenvectors according to the size of the eigenvalues;

　　3) According to the contribution ratio, find the subspace composed of larger eigenvectors;

　　4) The coordinates obtained by projecting each row of the original data X onto the subspace are the coordinates after dimension reduction;

　　5) Calculate the principal components.

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