Page 348 - Computational Statistics Handbook with MATLAB

Chapter 9: Statistical Pattern Recognition 337

muver = mean(versicolor);
covver = cov(versicolor);
% Those remain the same for the following.
for i = 1:nvir
% Get the test point and training set.
virtrain = virginica;
x = virtrain(i,:);
virtrain(i,:)=[];
muvir = mean(virtrain);
covvir = cov(virtrain);
pxgver = csevalnorm(x,muver,covver);
pxgvir = csevalnorm(x,muvir,covvir);
if pxgvir > pxgver
% then we correctly classified it
ncc = ncc+1;
end
end

Finally, the probability of correct classification is estimated using
pcc = ncc/n;
The estimated probability of correct classification for the iris data using
cross-validation is 0.68.

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We now turn our attention to how we can use cross-validation to evaluate a
classifier that uses the likelihood approach with varying decision thresholds
. It would be useful to understand how the classifier performs for various
τ C
thresholds (corresponding to the probability of false alarm) of the likelihood
ratio. This will tell us what performance degradation we have (in terms of
correctly classifying the target class) if we limit the probability of false alarm
to some level.
We start by dividing the sample into two sets: one with all of the target
observations and one with the non-target patterns. Denote the observations
as follows
1 ()
(
x i ⇒ Target pattern ω )
1
2 ()
x i ⇒ Non-target pattern ω 2 ).
(
denote
Let n 1 represent the number of target observations (class ω 1 ) and n 2
) patterns. We work first with the non-tar-
the number of non-target (class ω 2
get observations to determine the threshold we need to get a desired proba-
© 2002 by Chapman & Hall/CRC