Changeset 1181


Ignore:
Timestamp:
Feb 27, 2008, 10:31:28 PM (14 years ago)
Author:
Peter
Message:

fixes #262

Location:
trunk/doc
Files:
2 edited

Legend:

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  • trunk/doc/Statistics.doxygen

    r1159 r1181  
    304304\section Distance
    305305
    306 A Distance measures how far apart two ranges are. A Distance should
     306A \ref concept_distance measures how far apart two ranges are. A Distance should
    307307preferably meet some criteria:
    308308
     
    319319
    320320 - Having all unity weights should yield the unweighted case.
    321  - Rescaling invariant - \f$ w_i = Cw_i \f$ does not change the distance.
     321 - Rescaling the weights, \f$ w_i = Cw_i \f$, does not change the distance.
    322322 - Having a \f$ w_x = 0 \f$ the distance should ignore corresponding
    323323    \f$ x \f$, \f$ y \f$, and \f$ w_y \f$.
     
    329329   should equal to if you set \f$ w_{2i}=0 \f$.
    330330
    331 For a weighted distance, meeting these criteria, it might be difficult
    332 to show that the triangle inequality is fulfilled. For most algorithms
    333 the triangle inequality is not essential for the distance to work
    334 properly, so if you need to choose between fulfilling triangle
    335 inequality and these latter criteria it is preferable to meet the
    336 latter criteria. Here follows some examples:
    337 
    338 \subsection EuclideanDistance
    339 
    340 \subsection PearsonDistance
     331The last condition, duplicate property, implies that setting a weight
     332to zero is not equivalent to removing the data point. This behavior is
     333sensible because otherwise we would have a bias towards having ranges
     334with small weights being close to other ranges. For a weighted
     335distance, meeting these criteria, it might be difficult to show that
     336the triangle inequality is fulfilled. For most algorithms the triangle
     337inequality is not essential for the distance to work properly, so if
     338you need to choose between fulfilling triangle inequality and these
     339latter criteria it is preferable to meet the latter criteria.
    341340
    342341\section Kernel
  • trunk/doc/concepts.doxygen

    r1171 r1181  
    7070theplu::yat::statistics::EuclideanDistance.
    7171
     72\see \ref weighted_distance
     73
    7274*/
    7375
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