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Unformatted text preview: Statistical Pattern Recognition University of Maryland, College Park September 3, 2009 Professor Rama Chellappa Handout 1 Homework 1 This problem set is due Thursday September 10 at 11:00AM . 1. In a two-class one-dimensional problem, the pdfs are the Gaussians N (0 , 2 ) and N (1 , 2 ) for the two classes, respectively. Show that the threshold minimizing the average risk is equal to x = 1 / 2- 2 ln 21 P ( 2 ) 12 P ( 1 ) where 11 = 22 = 0 has been assumed. 2. Show that in a multiclass problem with M classes the probability of classification error for the optimum classifier is bounded by P e M- 1 M Hint: Show first that for each x the maximum of P ( i | x ) , i = 1 , 2 , . . ., M is greater that or equal to 1 /M . Equality holds if all P ( i | x ) are equal. 3. In a two-class classification task, we constrain the error probability for one of the classes to be fixed, that is, 1 = . Then show that minimizing the error probability of the other class results in the likelihood test...
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This note was uploaded on 10/26/2009 for the course CMSC 828 taught by Professor Staff during the Fall '05 term at Maryland.
- Fall '05