Distance Weighted Nearest Neighbor Algo

• weight the contribution of the neighbors by their distance, for instance the inverse square of the instances distance

• 

  where

  

• if the query point matches a training instance exactly the denominator will be 0 so we will just assign the value of that instance exactly
• for real-valued target functions the formula becomes

  

  where is defined as above

• note that if all the training instances return the same value, that value will also be returned by this formula
• weighted distance k-nearest neighbor can include all the instances, only the computation time necessary can be prohibitive - but then ``Nearest Neighbor'' becomes a global method (Shepard's method)