Examples of jmprojection.CDA

• jmprojection.CDA
  Henceforth:
  N-space means the original dimension of the data
  P-space or projection space means the space where data is projected by this algorithm, usually two dimensions.
  
  Curvilinear Distance Analysis algorithm.
  Algorithm by John Aldo Lee, Amaury Lendasse, Nicolas Donckers, Michel Verleysen
  in a article named "A Robust Nonlinear Projection Method"
  Published in ESANN'2000 proceedings, ISBN 2-930307-00-5, pp. 13-20
  
  In the algorithm we first quantizes the data-vectors in to centroids. Centroids represent space-averaged vectors in N-space.
  
  We then calculate distances in N-space between said centroid so that distance from centroid A to centroid B goes graph made out of centroids connecting to centroids near them.
  The distance between two centroids in N-space is therefore usually longer than just basic Euclidean distance. This distance is called curvilinear distance.
  
  We then project those centroids to P-space and try to keep Euclidean distances in P-space near curvilinear distances in N-space. This distance preservation is biased towards small distances by monotonically decreasing neighbourhood factor so that small distances come more and more significant and longer distances become less and less significant.
  This step is iterated for some more or less arbitrary times.
  
  After centroids have been projected in to P-space, we project the actual data-vectors and try to preserve their distances to centroids in the same way we tried to preserve inter-centroid distances in last step.
  After we've iterated this step for some more or less arbitrary times we're done.
  
  @author Jarkko Miettinen
  

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