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Gaussian Mixture Models

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Encyclopedia of Biometrics
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Synonyms

Gaussian mixture density; GMM

Definition

A Gaussian mixture model (GMM) is a parametric probability density function represented as a weighted sum of Gaussian component densities. GMMs are commonly used as a parametric model of the probability distribution of continuous measurements or features in a biometric system, such as vocal tract-related spectral features in a speaker recognition system. GMM parameters are estimated from training data using the iterative expectation-maximization (EM) algorithm or maximum a posteriori (MAP) estimation from a well-trained prior model.

Introduction

A Gaussian mixture model is a weighted sum of M component Gaussian densities as given by the equation

$$\displaystyle{ p\left (\left .\mathbf{x}\right \vert \uplambda \right ) =\sum \limits _{ i=1}^{M}w_{ i}g\left (\left .\mathbf{x}\right \vert \mu _{i},\boldsymbol{\upsigma }_{i}\right ), }$$
(1)

where x is a D-dimensional continuous-valued data vector (i.e., measurement or features); w...

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References

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Acknowledgements

This work was sponsored by the Department of Defense under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the US Government.

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Reynolds, D. (2015). Gaussian Mixture Models. In: Li, S.Z., Jain, A.K. (eds) Encyclopedia of Biometrics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7488-4_196

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