Page 46 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

DETECTION: THE TWO-CLASS CASE 35

1

0.8
measure of eccentricity 0.6

0.4

0.2

0
0 0.2 0.4 0.6 0.8 1
measure of 6–fold rotational symmetry
Figure 2.11 Bayes classification with the reject option included

Listing 2.5
PRTools code for minimum risk classification including a reject option

load nutsbolts;
cost ¼ [ 0.20 0.07 0.07 0.07 ; . . .
0.07 0.15 0.07 0.07 ; . . .
0.07 0.07 0.05 0.07 ; . . .
0.03 0.03 0.03 0.03 ; . . .
0.16 0.11 0.01 0.07 ];
clabels ¼ str2mat(getlablist(z),‘reject’);
w1 ¼ qdc(z); % Estimate a single Gaussian per class
scatterd(z);
% Change output according to cost
w2 ¼ w1*classc*costm([],cost’,clabels);
plotc(w1); % Plot without using cost
plotc(w2); % Plot using cost

2.3 DETECTION: THE TWO-CLASS CASE

The detection problem is a classification problem with two possible
classes: K ¼ 2. In this special case, the Bayes decision rule can be
moulded into a simple form. Assuming a uniform cost function the
MAP classifier, expressed in (2.12), reduces to the following test:

pðzj! 1 ÞPð! 1 Þ > pðzj! 2 ÞPð! 2 Þ ð2:34Þ