Timeline for Distance metric with characteristics of cosine and Manhattan
Current License: CC BY-SA 4.0
6 events
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| Feb 5, 2019 at 10:52 | history | edited | mapto | CC BY-SA 4.0 |
Removed redundant considerations based on the fact that the answer was accepted
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| Feb 5, 2019 at 10:00 | comment | added | mapto |
Regarding p1, notice that the number it operates on is before you apply atan. Thus, it is the Manhattan distance which - due to your components being integer - is integer and not necessarily in [0,1]. It was meant to balance for the fact that atan results in very close values for huge numbers. Take with a grain of salt, since today - one day later, the rationale behind this factor doesn't sound all that relevant to me either.
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| Feb 5, 2019 at 9:30 | vote | accept | jcp | ||
| Feb 5, 2019 at 9:29 | comment | added | jcp |
Thanks a lot! I like the idea of the atan, but I don't understand how it addresses your point. I understand that it is transforming the manhattan distance in the [0,1] domain. What I don't understand is how it addresses the problem of the difference of (1,0,0)-(0,0,0) vs (1000,0,0) - (999,0,0) for example. I also don't understand p1. It is raising a number in [0,1] to some power, so it will result in a smaller number in the same domain (for p1>1).
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| Feb 4, 2019 at 13:19 | history | edited | mapto | CC BY-SA 4.0 |
added 2 characters in body
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| Feb 4, 2019 at 13:02 | history | answered | mapto | CC BY-SA 4.0 |