Definition. A function f(x) is called scale-invariant if for every λ > 0, there exists a µ > 0 such that y = f(x) implies y′ = f(x′), where we denoted y′ = µ·y and x′ = λ · x. Proposition 1. For every two real numbers A and a, the function y = A · xa is scale-invariant.
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Scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor.
Size functions are integer valued functions of two real variables which represent metric and topological properties of visual shape. In this paper size ...
Scale invariance and the power law - Ellipsix Informatics
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Feb 7, 2012 · The point is that with a scale invariant function, it doesn't matter which reference value you choose. This is what makes these functions so ...
Mar 10, 2021 · "scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common ...
Nov 27, 2012 · Back in February I did a post on scale invariant functions of one variable. These are functions that satisfy the condition. f(λx)=C(λ)f(x).
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... size functions are invariant for every transformation preserving the measuring function. Hence, they can be adapted to many different applications, by ...
May 5, 2020 · I have some difficulties to prove that the above functions are scale-invariant according to Eq. [1], typically because of Eq. [1], I have a sum ...
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A scale-invariant optimization for a given function yields the same result for different parametrizations (i.e. scalings) of the function. E.g., for our toy ...
Sep 19, 2013 · So we could call a utility function scale invariant if there exist functions c:R>0→R and m:R>0→R>0 such that u(ax)=m(a)u(x)+c(a).