Machine Learning

Chapter 10

Gaussian Mixture Model

10.1 Introduction

As we know that each Gaussian is represented by a combination of mean and variance, if we have a mixture of M Gaussian distributions, then the weight of each Gaussian will be a third parameter related to each Gaussian distribution in a Gaussian mixture model (GMM). The following equation represents a GMM with M components.

p(x|θ)=∑k=1Mwkp(x|θk)

where w_k represents the weight of the kth component. The mean and covariance of kth components are represented by θ_k = (µ_k, ∑_k). p(x|θ_k), which is the Gaussian density of the kth component and is a D-variate Gaussian function of the following form:

p(x|θk)orp(x|(μk,∑k))=12πD/2|∑k|1/2e{−(1/2)(x−μk)′∑k−1(x−μk)}

Sum of values of w_k for different values ...