Abstract
Let X be a set. Let K(x, y) > 0 be a measure of the affinity between the data points x and y. We prove that K has the structure of a Newtonian potential K(x, y) = φ(d(x, y)) with φ decreasing and d a quasi-metric on X under two mild conditions on K. The first is that the affinity of each x to itself is infinite and that for x ≠ y the affinity is positive and finite. The second is a quantitative transitivity; if the affinity between x and y is larger than λ > 0 and the affinity of y and z is also larger than λ, then the affinity between x and z is larger than ν(λ). The function ν is concave, increasing, continuous from R+ onto R+ with ν(λ) < λ for every λ > 0
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© 2018 Ivana Gómez, published by De Gruyter
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