From: ajit_v_rROMEO@yahoo.co.uk   
      
   Hello,   
      
   I have a query about some of the extensions of the ISOMAP algorithm. I   
   basically have around N = 17000 points, each in D-dimensional space (D   
   being 400) which supposedly lie on a manifold. I wish to use ISOMAP to   
   project these points onto a d-dimensional space (d << D :  'd' could   
   be around 40 or less). My problem is that the basic ISOMAP algorithm   
   requires the computation (and storage) of a pairwise geodesic-distance   
   matrix, which in this case would be very large, i.e. 17000 * 17000. I   
   came to know about landmark ISOMAP, an extension of ISOMAP in which   
   one needs to compute the matrix of geodesic distances to only some   
   selected 'n' "landmark points" (where n << N).   
      
   My problem is that even this modification would still require me to   
   first compute a large N by N matrix of pairwise Euclidian distances   
   (and I will then apply Dijkstra's shortest path algorithm to obtain   
   the geodesic distances). Of course, I could keep computing the   
   Euclidian distances from one point to all others, every single time,   
   while running the Dijkstra's algorithm, but that is going to be very   
   time consuming.   
      
   Is there a way out?   
      
      
   (remove the shakespearean name to reply)   
      
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