Changeset 1181

Timestamp:

Feb 27, 2008, 10:31:28 PM (16 years ago)

Author:

Peter

Message:

fixes #262

Location:

trunk/doc

Files:

• Statistics.doxygen (modified) (3 diffs)
• concepts.doxygen (modified) (1 diff)

trunk/doc/Statistics.doxygen

@@ -304 +304 @@
 \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:
 
@@ -319 +319 @@
 
  - 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$.
@@ -329 +329 @@
    should equal to if you set \f$ 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

trunk/doc/concepts.doxygen

@@ -70 +70 @@
 theplu::yat::statistics::EuclideanDistance.
 
+\see \ref weighted_distance
+
 */