6. In many pattern classification problems one has the option either to assign the pat- tern to one of Ne classes, or to reject it as being unrecognizable. Let o,, i = 1,..., Ne be the action of...

Extracted text: 6. In many pattern classification problems one has the option either to assign the pat- tern to one of Ne classes, or to reject it as being unrecognizable. Let o,, i = 1,..., Ne be the action of deciding that the true state of nature is wi, and let o Net1 be the action of rejecting the pattern as unrecognizable. Let the loss function be 0, i = j A, i = Ne +1 d., otherwise where A, and A, are non-negative constants; A, is the loss associated with rejection, and A, is the loss associated with a wrong classification. Show that the minimum risk decision rule is to decide w, if P(w, x) > P(w,x) for all j and if P(w; x) >1-A/A., and reject otherwise. What happens in A, = 0? What happens if A, > 1,?