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# mcuturi

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## Registered User

 Name mcuturi Member for 2 years Seen Jun 10 at 22:06 Website Location Kyoto Age
 Apr29 comment how do you call a function that satisfies the metric axioms except for the coincidence axiom?And to answer Pietro, I plan to use that in a machine learning context, so it's an applied problem. I'll probably stick to $1_{x\ne y} d(x,y)$ to turn it (somewhat artificially, I agree) into a distance. Apr29 comment how do you call a function that satisfies the metric axioms except for the coincidence axiom?Thanks for all your comments! I gave it some extra thought. I see two links: negative definite kernels (in the sense of [Berg Christensen Ressel](books.google.co.jp/books/about/…). They consider negative definite kernels $\psi$ (p.82) that may not be such that $\psi(x,x)=0$. Negative definite kernels and distances are different, but they are somewhat related (the bigger, the more different). The other thing that's easy to check is that $1_{x\ne y} d(x,y)$ is itself a distance. It's not continuous.. but still a distance! Apr28 asked how do you call a function that satisfies the metric axioms except for the coincidence axiom?