Dimensionality Reducing by Alpha-Dense Curves ... - RUA

Definition
Let , be the spaces of continuous and bounded real functions , respectively on
. and a subset of .We say that a mapping , , is a
Minimization-Preserving Operator if and only if for any ,
i) the minimizer set of , denoted , is contained in the minimizer set of g, denoted ,
ii) and have at least a global minimum in common to both functions and g
Trivial examples of minimization-preserving operators in are:
a) The exponential operator,
b) The dilation operator, with. real numbers
In general, any strictly increasing function defines a M.P.O. on the space by
means of the composition law, that is, , for .
.