Encoding the position information in real distance metric












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The Euclidean distance doesn't preserve the exact position information. For example, the distance of the points (3,1) and (1,3) would be the same from the origin. Is there any distance metric which can encode the position information in a single real value, meaning the distance would be different for each point with respect to origin?










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    $begingroup$


    The Euclidean distance doesn't preserve the exact position information. For example, the distance of the points (3,1) and (1,3) would be the same from the origin. Is there any distance metric which can encode the position information in a single real value, meaning the distance would be different for each point with respect to origin?










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      $begingroup$


      The Euclidean distance doesn't preserve the exact position information. For example, the distance of the points (3,1) and (1,3) would be the same from the origin. Is there any distance metric which can encode the position information in a single real value, meaning the distance would be different for each point with respect to origin?










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      $endgroup$




      The Euclidean distance doesn't preserve the exact position information. For example, the distance of the points (3,1) and (1,3) would be the same from the origin. Is there any distance metric which can encode the position information in a single real value, meaning the distance would be different for each point with respect to origin?







      geometric-invariant-theory mahalanobis-distance hausdorff-distance






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      asked Dec 11 '18 at 10:52









      anonanon

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          Yes.



          Pick your favourite bijection (or at least injection) $fcolon Bbb R^2to [0,infty)$ such that $fbigl((0,0)bigr)=0$ and declare $d(a,b)=|f(a)-f(b)|$.






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            $begingroup$

            Yes.



            Pick your favourite bijection (or at least injection) $fcolon Bbb R^2to [0,infty)$ such that $fbigl((0,0)bigr)=0$ and declare $d(a,b)=|f(a)-f(b)|$.






            share|cite|improve this answer









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              $begingroup$

              Yes.



              Pick your favourite bijection (or at least injection) $fcolon Bbb R^2to [0,infty)$ such that $fbigl((0,0)bigr)=0$ and declare $d(a,b)=|f(a)-f(b)|$.






              share|cite|improve this answer









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                $begingroup$

                Yes.



                Pick your favourite bijection (or at least injection) $fcolon Bbb R^2to [0,infty)$ such that $fbigl((0,0)bigr)=0$ and declare $d(a,b)=|f(a)-f(b)|$.






                share|cite|improve this answer









                $endgroup$



                Yes.



                Pick your favourite bijection (or at least injection) $fcolon Bbb R^2to [0,infty)$ such that $fbigl((0,0)bigr)=0$ and declare $d(a,b)=|f(a)-f(b)|$.







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                answered Dec 11 '18 at 12:09









                Hagen von EitzenHagen von Eitzen

                280k23272505




                280k23272505






























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