For the original data, the minimum error criterion should be satisfied in the process of dimension reduction. Suppose the first a feature values are considered. The estimated value of the corresponding reconstruction is

( X , X ) ¯ = i=1 n ( Y i , Y i )( M i , M i )( 4.16 )

The average variance is

( e a , e a )=E[ ( ( X , X ) ( X , X ) ¯ ) 2 ]= l=a+1 n ( λ i , λ i ).( 4.17 )

When the a-eigenvalues of the ( X , X ) autocovariance matrix become larger, the mean square error becomes smaller. Thus, it is easy to find principal component whereby ...

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