781405779_1_homework2 - Assignment of "Pattern...

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Assignment of “Pattern Recognition” (Ch.2 Bayes Decision Theory) 1 Prove that Mahalanobis metric (distance) indeed possesses the four properties required of all metrics (distances), i.e. r (1) Nonnegativity: ( ) ,0 rab (2) Reflexivity: ()() ,, rab rba = (3) Symmetry: () , 0 if and only if a b == (4) Triangle Inequality: ( ) rac rab rbc ≤+ , 2. Consider two-dimensional Gaussian distribution, ( ) 12 1, 0 , , TT =− = μμ 11 2 1 1 2 , 1 1 ⎡⎤ Σ= ⎢⎥ ⎣⎦ 2 and () () 1 PP ϖ = . Give the decision rule in form of
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781405779_1_homework2 - Assignment of "Pattern...

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