Autoscaling is a combination of unit variance scaling and mean-centering: First the standard deviation and the avarage value of each column are calculated. Then the mean value ist substracted from the data and the result is divided by the standard deviation.

The following lines give the procedure for Autoscaling the x(i,j) values of each column of an n x m data matrix with additional columns of dependent y(i):

x(1,1)   x(2,1) . . . x(n,1)  y(1)
x(1,2)   x(2,2) . . . x(n,2)  y(2)
x(1,m)   x(2,m) . . . x(n,m)  y(m)

The new independent values z(i,,j) are calculated as follows:


where m(i) is the mean value of column i (for centering) and

is the standard deviation

of column i (for scaling). The last column remains unchanged.