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In many pattern classification problems óné pattern to one of c classes, or to reject it as being unrecognizable. If the cost for rejects is not too high, rejection may be a desirable action. Let i, j = 1, ..., c i = j i =c+1 otherwise, %3D

In many pattern classification problems óné pattern to one of c classes, or to reject it as being unrecognizable. If the cost for rejects is not too high, rejection may be a desirable action. Let i, j = 1, ..., c i = j i =c+1 otherwise, %3D

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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1. Duda, problem 2.13. Secion 4.4 13. In many pattern classification problems one has the option either to assign the pattern to one of c classes, or to reject it as being unrecognizable. If the cost for rejects is not too high, rejection may be a desirable action. Let i, j = 1,..., c { i = j i =c+1 otherwise, %3D where , is the loss incurred for choosing the (c + 1)th action, rejection, and is the loss incurred for making any substitution error. Show that the minimum risk is obtained if we decide wi if P (w,\x) > P(wj|x) for all j and if P(@\x) Z 1- 1,/A,, and reject otherwise. What happens if 2, = 0? What happens if 1, > 1,? %3D
Transcribed Image Text:1. Duda, problem 2.13. Secion 4.4 13. In many pattern classification problems one has the option either to assign the pattern to one of c classes, or to reject it as being unrecognizable. If the cost for rejects is not too high, rejection may be a desirable action. Let i, j = 1,..., c { i = j i =c+1 otherwise, %3D where , is the loss incurred for choosing the (c + 1)th action, rejection, and is the loss incurred for making any substitution error. Show that the minimum risk is obtained if we decide wi if P (w,\x) > P(wj|x) for all j and if P(@\x) Z 1- 1,/A,, and reject otherwise. What happens if 2, = 0? What happens if 1, > 1,? %3D
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