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Lecture 02 Nearest Neighbor Methods STAT 479: Machine Learning, Fall 2018 Sebastian Raschka http://stat.wisc.edu/~sraschka/teaching/stat479-fs2018/ 1
1-Nearest Neighbor Prediction Step closest_point := None closest_distance := for : current_distance := if current_distance < closest_distance: closest_distance := current_distance closest_point := return closest_point closest_point is the label of Sebastian Raschka STAT 479: Machine Learning FS 2018 !5
Commonly used: Euclidean Distance (L2) m 2 d(x[a],x[b]) = x[a] − x[b] ∑( j j ) j=1 Sebastian Raschka STAT 479: Machine Learning FS 2018 !6
a a Decision Boundary Between (a) and (c) d c Sebastian Raschka STAT 479: Machine Learning FS 2018 !10
Which Point is Closest? Euclid distan a c ? b Sebastian Raschka STAT 479: Machine Learning FS 2018 !13
a ? a ? b b Depends on the Distance Measure! Euclidean distance=1 Manhattan distance=1 a c ? ? b Sebastian Raschka STAT 479: Machine Learning FS 2018 !14
Continuous Distance Measures Euclidean Manhattan 1 Minkowski: m p p d(x[a],x[b]) = x[a] − x[b] [∑( ) ] j=1 Mahalanobis ... Sebastian Raschka STAT 479: Machine Learning FS 2018 !15
Discrete Distance Measures m Hamming: d(x[a],x[b]) = ∑ x[a] − x[b] j=1 Jaccard/Tanimoto Cosine similarity Dice ... Sebastian Raschka STAT 479: Machine Learning FS 2018 !16
Feature Scaling Euclidean Euclidean distance=1 distance=1 c c a ? a ? b b Euclidean Sebastian Raschka STAT 479: Machine Learning distance=1FS 2018Manhattan !17 distance=1
A y: Majority vote: Purality vote: B y: Majority vote: None Purality vote: Sebastian Raschka STAT 479: Machine Learning FS 2018 !19
kNN for Classification 𝒟 = {⟨x[1], f(x[1])⟩,…,⟨x[k], f(x[k])⟩} 𝒟k ⊆ 𝒟 k Sebastian Raschka STAT 479: Machine Learning FS 2018 !20
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