Changeset 1181 for trunk/doc/Statistics.doxygen
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 Feb 27, 2008, 10:31:28 PM (15 years ago)
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trunk/doc/Statistics.doxygen
r1159 r1181 304 304 \section Distance 305 305 306 A Distance measures how far apart two ranges are. A Distance should306 A \ref concept_distance measures how far apart two ranges are. A Distance should 307 307 preferably meet some criteria: 308 308 … … 319 319 320 320  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$, does not change the distance. 322 322  Having a \f$ w_x = 0 \f$ the distance should ignore corresponding 323 323 \f$ x \f$, \f$ y \f$, and \f$ w_y \f$. … … 329 329 should equal to if you set \f$ w_{2i}=0 \f$. 330 330 331 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 331 The last condition, duplicate property, implies that setting a weight 332 to zero is not equivalent to removing the data point. This behavior is 333 sensible because otherwise we would have a bias towards having ranges 334 with small weights being close to other ranges. For a weighted 335 distance, meeting these criteria, it might be difficult to show that 336 the triangle inequality is fulfilled. For most algorithms the triangle 337 inequality is not essential for the distance to work properly, so if 338 you need to choose between fulfilling triangle inequality and these 339 latter criteria it is preferable to meet the latter criteria. 341 340 342 341 \section Kernel
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