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# hw2 - EE 649 Pattern Recognition Spring 2008 Homework 2 Due...

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EE 649 Pattern Recognition – Spring 2008 Homework 2 Due on: Feb 29 Homework Policy : Please return homework in my mailbox by 5 p.m. on Feb 29. 1. Solve Problem 2.9 in DHS. 2. Solve Problem 2.27 in DHS. 3. Solve Problem 2.32 in DHS. Hint: Rotate and translate the coordinate system so that the axis joining the means coincides with one of the axes. You do not need to specify the translation or rotation matrix explicitly. 4. Solve Problem 4.8 in DHS. Hint: Here, P denotes the same as e NN , the asymptotic classification error for the 1-NN classifier. For arbitrary number of classes ( c> 2), it is given by equation (45) in DHS. For example, for c = 3, P = E [1 ( η 1 ( X ) 2 + η 2 ( X ) 2 + η 3 ( X ) 3 ] , where η i ( X ) = P ( Y = i | X ). For c = 2, this reduces to what we discussed in class (you can check it). The bayes error for an arbitrary number of classes is given by: ǫ = E [1 max i η i ( X )] . For c = 2, this reduces to the familiar expression we have been discussing. The key to this

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