Page 353 - Computational Statistics Handbook with MATLAB

342 Computational Statistics Handbook with MATLAB

For the given thresholds, we now find the probability of correctly classifying
the target cases. This corresponds to steps 8 through 13.

% Now find the probability of correctly
% classifying targets.
mu2 = mean(x2);
var2 = cov(x2);
% Do cross-validation on target class.
for i = 1:n1
train = x1;
test = x1(i);
train(i) = [];
mu1 = mean(train);
var1 = cov(train);
lr1(i) = csevalnorm(test,mu1,var1)./...
csevalnorm(test,mu2,var2);
end
% Find the actual pcc.
for i = 1:length(pfa)
pcc(i) = length(find(lr1 >= thresh(i)));
end
pcc = pcc/n1;
The ROC curve is given in Figure 9.9. We estimate the area under the curve
as 0.91, using

area = sum(pcc)*.01;

9.4 Classification Trees
In this section, we present another technique for pattern recognition called
classification trees. Our treatment of classification trees follows that in the
book called Classification and Regression Trees by Breiman, Friedman, Olshen
and Stone [1984]. For ease of exposition, we do not include the MATLAB code
for the classification tree in the main body of the text, but we do include it in
Appendix D. There are several main functions that we provide to work with
trees, and these are summarized in Table 9.1. We will be using these functions
in the text when we discuss the classification tree methodology.
While Bayes decision theory yields a classification rule that is intuitively
appealing, it does not provide insights about the structure or the nature of the
classification rule or help us determine what features are important. Classifi-
cation trees can yield complex decision boundaries, and they are appropriate
for ordered data, categorical data or a mixture of the two types. In this book,
© 2002 by Chapman & Hall/CRC