12-hyperplanes - Example Majority-Vote Function Foundations...

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1 Foundations of Artificial Intelligence Perceptrons and Optimal Hyperplanes CS472 – Fall 2007 Thorsten Joachims 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 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. Linear Classification Rules Hypotheses of the form – unbiased: – biased: Parameter vector w, scalar b Hypothesis space H Notation Geometry of Hyperplane Classifiers
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