Implementation of Locally Weighted Learning

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Implementation of Locally Weighted Learning
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k-d Trees

• Binary search tree
• k of dimensions/attributes
• of data points
• Search for nearest neighbor in k-dimensional
  space
• Used in Database systems
• Very fast (distance computations less than n)

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k-d Trees

• Layer i modulo k discriminates regarding
  dimension I
• 2-d Tree
• Points tupel (x,y)
• left son
  right son
• Layer with odd number every key lt x
  every key gt x
• Layer with even number every key lty
  every key gty

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Insertion into k-d Tree
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2-d Tree
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2-d-Tree nearest neighbor search(shrinking range
query)
Best match for P(7/3).
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2-d Tree nearest neighbor search

• Only a few nodes need to be inspected
• Problem, when Data is uniformly distributed

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References

• C.G.Atkeson, A.W.Moore, S.Schaal, Locally
  Weighted Learning, Artificial Intelligence
  Review, 1111-73, 1997