Mean-Centering, Scaling, and Autoscaling

Mean-centering, as is shown by experience, can be successfully employed in combination with another data pre-processing technique, namely scaling, which is discussed later. 

Xy is the ith entry of the jth column vector and n is the number of objects (rows in the matrix). The essence of mean-centering is to subtract this average from the entries of the vector (Eq. (6)). 

What we have now is the resultant data matrbf containing the coliunn vectors with the average values each being zero. 

The result is that each column vector has unit standard deviation. 

What UV-scaling does is to concentrate the relevant information into the same range for all the variables (or, at least, for those subjected to this method). Then, the loading matrix yielded by PCA will show the importance of the initial variables. 

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