Page 350 - Computational Statistics Handbook with MATLAB

Chapter 9: Statistical Pattern Recognition 339

0.25

Decision Region Decision Region
Target Class Non−target Class
0.2

0.15

TP TN
0.1

0.05

TN TP
+FP +FN
0
−6 −4 −2 0 2 4 6 8
Feature − x
U
FI F IG URE G 9. RE 9. 8 8
GU
8
F F II GU RE RE 9. 9. 8
In this figure, we see the decision regions for deciding whether a feature corresponds to the
target class or the non-target class.
P x ω 1 )
(
L R x() = -------------------- .
(
P x ω 2 )
We start off by forming the likelihood ratios using the non-target ω 2 ) obser-
(
vations and cross-validation to get the distribution of the likelihood ratios
. We use these likelihood ratios to set
when the class membership is truly ω 2
the threshold that will give us a specific probability of false alarm.
Once we have the thresholds, the next step is to determine the rate at which
we correctly classify the target cases. We first form the likelihood ratio for
each target observation using cross-validation, yielding a distribution of like-
lihood ratios for the target class. For each given threshold, we can determine
the number of target observations that would be correctly classified by count-
that are greater than that threshold. These steps are
ing the number of L R
described in detail in the following procedure.

CROSS-VALIDATION FOR SPECIFIED FALSE ALARM RATE

(non-
1. Given observations with class labels ω 1 (target) and ω 2
target), set desired probabilities of false alarm and a value for k.

© 2002 by Chapman & Hall/CRC