Resolution:
## 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 X_{1} and X_{2}with an angle θ. By now, two original correlated variables(X_{1}, X_{2})were transformed into two integrated and uncorrelated variables (Y_{1,}Y_{2}). Because the variance of the original variables is greater in Y_{1} axis than in Y_{2} axis, so the minimum of information will be lost if integrated variable Y_{1} is used for replacing all original variables. Hence,Y_{1} is defined as the first principal component; in contrast, variance of variables is
smaller in Y_{2} axis, and it can explain minor information relative to Y_{1}, soY_{2} is called the second principal component.
Zhao |