Introduction to Pattern Recognition: A Matlab Approach

1.5 Mixture Models 11

1.5 MIXTURE MODELS

When the pdf that describes the data points in a class is not known, it has t o be estimated prior to

the application of the Bayesian classifier. In this sect i on, we focus on a very popular met hod t o model

unknown probability density functions, known as mixture modeling [Theo 09, Section 2.5.5].

An arbitrary pdf can be modeled as a linear combination of J pdfs in the form

p(x) =

J



j=1

P

j

p(x|j) (1.6)

where

J



j=1

P

j

=1,



p(x|j)dx =1

for sufficiently large J. In most cases, p(x|j) are chosen to be Gaussians, N (m

j

,S

j

), j = 1, 2,..., J.

The expansion i n Eq. (1.6) points out a way to generate data from pdfs of a more ...