12_HyperPlanes

# 12_HyperPlanes - Example MajorityVote Function Definition...

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10/21/2009 1 Perceptrons and Optimal Hyperplanes Example: Majority Vote Function Definition: Majority Vote Function f majority N binary attributes, i.e. x {0,1} N If more than N/2 attributes in x are true, then f (x)=1 else f (x)= 1 majority (x)=1, else f majority (x)= 1. How can we represent this function as a decision tree? Huge and awkward tree! Is there an “easier” representation of f majority ? Example: Spam Filtering Instance Space X: Feature vector of word occurrences => binary features N features (N typically > 50000) Target Concept c: Spam (+1) / Ham ( 1) Type of function to learn: Set of Spam words S, Set of Ham words H Classify as Spam (+1), if more Spam words than Ham words in example. Example: Spam Filtering Use weight vector w=(+1, 1, 0, +1, +1) Compute sign(wx) • More generally, we can use real valued weights to express “spamminess” of word. • w=(+10, 1, 0.3,+1,+5) • Which vector is most likely to be spam with this weighting? A=x 1 , B=x 2 , C=x 3

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