Changeset 1181 for trunk/doc/Statistics.doxygen

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Timestamp:
Feb 27, 2008, 10:31:28 PM (14 years ago)
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fixes #262

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