A distance function which scales with the value size

Question

This is a math question related to machine learning.

I have a data set I want to cluster and to do this I want to define a bespoke distance function. My understanding of the data is that the distance between numerical values depends on the scale. That is 9 is not very close to 10 but 900 is very close to 901.

Is there a natural mathematical distance function (or transformation) that encapsulates this intuition? Ideally it would be parameterized so I can grid search to find good distance functions.

score 0 · Answer 1 · answered Sep 27 '15 at 14:16

0

you could define a relative measure of distance: D = V1 / V2 - 1 Using this, D = 9 / 10 -1 = -0.1 , that is, 9 is 10% lesser than 10. Another example, D = 201 / 200 -1 = 0.005 , that is, 201 is 5% bigger than 200. Obviously this definition doesn't work if your reference V2 is zero.

answered Sep 27 '15 at 14:16

user87387

1

Correcting a mistake: "... 201 is 0,5% bigger than 200." – user87387 Sep 27 '15 at 14:26
Thank you. How could you parameterize this? – Sep 27 '15 at 15:53
What do you mean by parametrize? – user87387 Sep 27 '15 at 19:10
I just meant change how much scale affects the answer. For example make 9 relatively closer to 10 or further away. – Sep 27 '15 at 20:13

A distance function which scales with the value size

1 Answers1