Describe Generalized principal components analysis, Advanced Statistics

Generalized principal components analysis: The non-linear version of the principal components analysis in which the goal is to determine the non-linear coordinate system which is most in agreement with the data configuration. For instance, for the bivariate data, y1,y2, if the quadratic coordinate system is sought, a variable z is defined as given below:

127_generalized principal component analysis.png 
with the coefficients being set up so that the variance of z is a maximum amongst all such quadratic functions of y1 and y2.

 

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