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Jan 16, 2015 at 8:04 comment added Włodzimierz Holsztyński Hm, naively, my definition may define a topologically weaker metrics. In my case I do two fittings--left and righ--independently, while your (Yohei's) fitting is simultaneous. Perhaps the difference is not essential, and perhaps it's trivial to prove that the two metric definitions are equivalent.
Jan 16, 2015 at 2:38 history edited Włodzimierz Holsztyński CC BY-SA 3.0
Just a free monoid.
Jan 15, 2015 at 15:03 comment added Włodzimierz Holsztyński Actually, your definition seems to be equivalent to mine. Mine is just more complicated. I'll look at this later, and most likely I will remove my answer.
Jan 15, 2015 at 14:58 history edited Włodzimierz Holsztyński CC BY-SA 3.0
cleaning up
Jan 15, 2015 at 14:45 history edited Włodzimierz Holsztyński CC BY-SA 3.0
about the generality
Jan 15, 2015 at 14:43 comment added Włodzimierz Holsztyński Thank you, Yohei. I may add some words if the formulas are not edible enough.
Jan 15, 2015 at 13:33 history answered Włodzimierz Holsztyński CC BY-SA 3.0