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Machine Learning by Eihab Mohammed Bashier, Muhammad Badruddin Khan, Mohssen Mohammed

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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 wk represents the weight of the kth component. The mean and covariance of kth components are represented by θk = (µk, ∑k). p(xk), which is the Gaussian density of the kth component and is a D-variate Gaussian function of the following form:

p(x|θk)or p(x|(μk,k))=12πD/2|k|1/2e{(1/2)(xμk)k1(xμk)}

Sum of values of wk for different values ...

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