From: project2501@project2501.cor   
      
   to continue with the development of the clustering algorithm over fuzzy   
   data (memberships of) ...   
      
   i now realise that there are two mathematical hurdles to get over when   
   generalising the standard k-means to data instances which are essentially   
   vectors of "ordered" vectors (see previous posts).   
      
   i am happy with the method discussed in the earlier posts to this thread   
   on a distance measure for such data instances. i'm even happy to use the   
   slightly inelegant adjustments to ensure some kindo f "ordering" (again,   
   see previous posts).   
      
   however, the next, and i beleive final, hurdle is that the k-means   
   algorithm requires that the "centre of mass" of a group of data instances   
   be calculated during its iterative updating. this concept of a centre of   
   mass is something i am now thinking about in relation to such data. to   
   repeat anexample of such data :   
      
   x1 = {feature1: A1 + B1 + C1,   
         feature2: D1 + E1}   
      
   x2 = {feature1: A2 + B2 + C2,   
         feature2: D2 + E2}   
      
   any thoughts, or previous experience, on this would be gratefully   
   receieved.   
      
   my pre-initial thoughts are somthing along the lines of   
      
       COM(x1) = sum(  distance(x_i, projection(X_i onto x1 axis)) )   
      
   but i'll go away and think about it...   
      
   p   
      
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