Introduction to Pattern Recognition: A Matlab Approach

2 CHAPTER 1 Classifiers Based on Bayes Decision Theory

According to the Bayes decision theory, x i s assigned to t he class ω

i

if

P(ω

i

|x)>P(ω

j

|x), ∀j = i (1.2)

or, taking i nto account Eq. (1.1) and given that p(x) is positive and the same for all classes, if

p(x|ω

i

)P(ω

i

)>p(x|ω

j

)P(ω

j

), ∀j =i (1.3)

Remark

• The Bayesian classifier is optimal in the sense that it minimizes the probability of error [Theo 09,

Chapter 2].

1.3 THE GAUSSIAN PROBABILITY DENSITY FUNCTION

The Gaussian pdf [Theo 09, Section 2.4.1] is extensively used in pattern recognition because of its

mathematical tractability as well as because of the central limit theorem. The latter states ...