Nearest neighbor methods Lecture 11 David Sontag New - PowerPoint PPT Presentation

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Nearest neighbor methods Lecture 11 David Sontag New York University Slides adapted from Vibhav Gogate, Carlos Guestrin, Mehryar Mohri, & Luke Zettlemoyer Nearest Neighbor Algorithm

Nearest ¡neighbor ¡methods ¡ Lecture ¡11 ¡ David ¡Sontag ¡ New ¡York ¡University ¡ Slides adapted from Vibhav Gogate, Carlos Guestrin, Mehryar Mohri, & Luke Zettlemoyer
Nearest ¡Neighbor ¡Algorithm ¡ • Learning ¡Algorithm: ¡ – Store ¡training ¡examples ¡ • Predic@on ¡Algorithm: ¡ – To ¡classify ¡a ¡new ¡example ¡ x ¡by ¡finding ¡the ¡training ¡ example ¡( x i ,y i ) ¡that ¡is ¡ nearest ¡to ¡ x ¡ – Guess ¡the ¡class ¡y ¡= ¡y i ¡
K-‑Nearest ¡Neighbor ¡Methods ¡ To ¡classify ¡a ¡new ¡input ¡vector ¡x, ¡examine ¡the ¡k-‑closest ¡training ¡data ¡points ¡to ¡x ¡ • and ¡assign ¡the ¡object ¡to ¡the ¡most ¡frequently ¡occurring ¡class ¡ k=1 k=5 x common values for k: 3, 5
Decision ¡Boundaries ¡ The ¡nearest ¡neighbor ¡algorithm ¡does ¡not ¡explicitly ¡compute ¡decision ¡ • boundaries. ¡ ¡However, ¡the ¡decision ¡boundaries ¡form ¡a ¡subset ¡of ¡the ¡Voronoi ¡ diagram ¡for ¡the ¡training ¡data. ¡ The more examples that are stored, the more complex the decision boundaries  can become

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