Constructing new features via linear combination so that classification is easier. The notion of "easier" is quantified by Fisher's criterion, which applies exactly to Gaussian classes with equal variance and approximately to other models. Variants like Flexible discriminant analysis consider nonlinear combinations as well. See Duda&Hart, "Eigenfaces vs. Fisherfaces", and "Flexible Discriminant and Mixture Models".

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett