From: mailbox@dmitry-kazakov.de   
      
   On Sun, 13 Apr 2008 04:54:30 GMT, DrColombes wrote:   
      
   > Probabilistic likelihood "distance" functions compute well with   
   > missing or multiple observations of real-valued functions, but how   
   > should a metric distance function (e.g., Euclidean distance) handle   
   > missing or multiple observations?   
   >   
   > Assuming a worst-case difference for missing attributes would seem to   
   > dilute the discrimination ability of the observed attributes, and   
   > averaging multiple observations would seem to reduce the contribution   
   > of multiple observations.   
   >   
   > Thanks for your comments, suggestions.   
      
   1. You could do add ideal elements to the space in order to have a value of   
   a missing attribute.   
      
   2. You could make the distance taking values from another set instead of R.   
   It could be [0,1]^R (fuzzy numbers), or something like that.   
      
   3. You could switch to set distances. Each observation would an element of   
   a set. Missing attributes could be modeled as all possible values of the   
   attribute (a plane).   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
   [ comp.ai is moderated ... your article may take a while to appear. ]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)