11_distances

# Choose the label that occurs among the majority of

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Unformatted text preview: ume that is between r=1-ε and r=1. Why do you expect this to work better? Vd ( r ) = k d · r d The required fraction is: Vd (1) Related fact: Vd (1 Vd (1) ✏) =1 (1 ✏)d The ratio of the volume of the unit sphere and unit cube tends to 0 as d goes to inifnity. 23 6 10/21/13 k-NN k-NN Use the closest k neighbors to make a decision instead of a single nearest neighbor Use the closest k neighbors to make a decision instead of a single nearest neighbor Choose the label that occurs among the majority of the k nearest neighbors Choose the label that occurs among the majority of the k nearest neighbors Can produce confidence scores. How? Other refinements: an example’s vote is inversely proportional to its distance NN vs k-NN Nearest neighbor regression How do turn k-NN into a regression method? The data Using 1 NN Using 5 NN white regions occur where there ties Images from http://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm 28 7 10/21/13 Distances and kernels Distances and kernels The Euclidean dista...
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