Figure 1.

Geometric meaning of PCA explained by using bivariate normally distributed variables. Scatters of sample are distributed in the shape of ellipse roughly, then orthogonally rotate the original plane rectangular coordinates composed of X₁ and X₂with an angle θ. By now, two original correlated variables(X₁, X₂)were transformed into two integrated and uncorrelated variables (Y_1,Y₂). Because the variance of the original variables is greater in Y₁ axis than in Y₂ axis, so the minimum of information will be lost if integrated variable Y₁ is used for replacing all original variables. Hence,Y₁ is defined as the first principal component; in contrast, variance of variables is smaller in Y₂ axis, and it can explain minor information relative to Y₁, soY₂ is called the second principal component.