PCA Calculations Demonstrated with a Simple Example

We take the same example as used in Section 5.3.4 for cluster analysis  

The elements of R are the (bivariate) correlation coefficients riU2 of each feature pair (xn, xi2) introduced in Section 2.4.2 as the covariance sjla of two features standardized by both standard deviations siU2. riU2 = sfu2 /(.v,i sl2). 

The eigenvalues, 2, of this correlation matrix are obtained by solving the characteristic determinant (Eq. 5-18 is repeated for easier understanding), i.e.  

The eigenvectors e connected with the two eigenvalues are computed from the equations  

Now with both eigenvalues X and factor loadings a one decomposes (or reconstructs) matrix R according to 

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