Page 84 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

72 Chapter 2

The computed values are the current best estimates of means and
covariance matrices. Using this Expectation stage is executed, followed by
Maximization stage. Thus Expectation stage and Maximization stage is
repeated for N iterations and hence best estimate of the means and
covariance matrices are obtained using E-M algorithm.
Using the estimated means p(c 1), p(c 2), p(c 3)…p(c n) are obtained and
hence the Gaussian Mixture Model of the collected is obtained.

2.2 Example

Two dimensional vectors are randomly generated and the Gaussian
Mixture Model of the generated data is obtained using the algorithm
described above is displayed below.
About 350 vectors are randomly generated. Among which 100 vectors
are with mean [0.9 0.8], 100 vectors are with mean [0.7 0.6] and 150 vectors
are with mean [0.5 0.4].
The elements of the individual vector are generated independently and
hence the estimated covariance matrices are diagonal in nature.
Estimated values of the GMM model after 10 Iterations are given below

Mean vector 1 = [0.9124 0.7950]
Mean vector 2 = [0.7125 0.6091]
Mean vector 3 = [0.4994 0.3990]

Covariance matrix 1
0.0045 -0.0001
-0.0001 0.0047

Covariance matrix 2
0.0048 -0.0003
-0.0003 0.0048

Covariance matrix 3
0.0055 -0.0005
-0.0005 0.0054