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L4 - EE7750 Lecture4:Bayes Discriminant Let us examine the...

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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 ( ) ln ( | ) ln ( ) i i i g p w P w = + x x ( ) ( | ) ~ , i i i p w N x μ Σ ( ) ( ) 1 / 2 1/ 2 1 1 ( ) ln exp ln ( ) (2 ) | | 2 T i i i i i d i g P w π = + x x μ Σ x μ Σ ( ) ( ) 1 1 1 ( ) ln 2 ln ln ( ) 2 2 2 T i i i i i i d g P w π = − + x x μ Σ x μ Σ
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Discriminant Functions for Gaussian Case I: 2 i σ = Σ I ( ) 1 2 1/ i σ = Σ I ( ) ( ) 2 1 ( ) ln ( ) 2 T i i i i g P w σ = − + x x μ x μ
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Discriminant Functions for Gaussian Case I: 2 i σ = Σ I ( ) 1 2 1/ i σ = Σ I ( ) ( ) 2 1 ( ) ln ( ) 2 T i i i i g P w σ = − + x x μ x μ As the priors change, the decision boundaries shift.
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