PRML-RS-Chapter 4 Linear Classifier

PRML-RS-Chapter 4 Linear Classifier - Pattern Recognition...

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Hong [email protected] 1 Pattern Recognition and Machine Learning ---- For Remote-Sensing Images Hong TANG Beijing Normal University
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Hong [email protected] 2 Before we get started. ..
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Hong [email protected] 3 Chapter 4. Linear Classifier Linear Discriminant Functions Parameter Estimation Generalized Linear Discriminant Functions
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Hong [email protected] 4 Linear discriminant functions A linear classifier is a function that is a linear combination of the components of x g(x) = w t x + w 0 where w is the weight vector and w 0 the bias
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Hong [email protected] 5 Linear discriminant functions and decisions surfaces Two-category problem ( ω 1 =+1, 2 =-1): decision boundary : g ( x ) = 0 correctly classification : g ( x ) > 0 distance to decision : () r gx w =
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Hong [email protected] 6 Two-category problem ( ω 1 =+1, 2 =-1): decision boundary : g ( x ) = 0 The equation g(x) = 0 defines the decision surface that separates points assigned to the category 1 from points assigned to the category 2 When g(x) is linear, the decision surface is a hyperplane Linear Classifier
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Hong [email protected] 7 Linear discriminant functions and decisions surfaces Two-category problem ( ω 1 =+1, 2 =-1): correctly classification : g ( x ) > 0 Decide 1 if g(x) > 0 and 2 if g(x) < 0 Decide 1 if w t x > -w 0 and 2 otherwise If g(x) = 0 x is assigned to either class
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Hong [email protected]
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This note was uploaded on 12/16/2010 for the course RESOURCE 148 taught by Professor Hongtang during the Spring '10 term at BUPT.

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PRML-RS-Chapter 4 Linear Classifier - Pattern Recognition...

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