L4 - EE7750 MACHINERECOGNITIONOFPATTERNS Lecture4:Bayes

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EE7750 MACHINE RECOGNITION OF PATTERNS Lecture 4: Bayes Classifiers for Gaussian Distributed Data
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Discriminant Functions for Gaussian Let us examine the discriminant function for () l n ( | ) l n ( ) ii i gp w P w =+ xx ( ) (| ) ~ , i pw N x μΣ ()() 1 /2 1/2 11 n e x p l (2 ) | | 2 T i i i d i gP w π ⎡⎤ =− + ⎢⎥ ⎣⎦ x μ Σ () 1 l n2 l n l 22 2 T i i i i d g Pw + x
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Discriminant Functions for Gaussian Case I: 2 i σ = Σ I ( ) 12 1/ i = Σ I () 2 1 l n ( ) 2 T ii i i gP w =− + xx μ x μ
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Discriminant Functions for Gaussian Case I: 2 i σ = Σ I ( ) 12 1/ i = Σ I () 2 1 l n ( ) 2 T ii i i gP w =− + xx μ x μ As the priors change, the decision boundaries shift.
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Discriminant Functions for Gaussian Case I: 2 i σ = Σ I ( ) 12 1/ i = Σ I () 2 1 l n ( ) 2 T ii i i gP w =− + xx μ x μ If all the prior probabilities are equal; then the classifier is equivalent to the Euclidean distance classifier.
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Discriminant
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This note was uploaded on 09/21/2010 for the course EE EE7750 taught by Professor Bahadirgunturk during the Fall '10 term at LSU.

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L4 - EE7750 MACHINERECOGNITIONOFPATTERNS Lecture4:Bayes

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