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,
where x is a D-dimensional continuous-valued data vector (i.e. measurement or features), w i , i = 1, …, M, are the mixture weights, and \(g({\bf x}\vert...
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Benesty, J., Sondhi, M., Huang, Y. (eds.): Springer Handbook of Speech Processing, vol. XXXVI. Springer, Berlin (2008)
Müler, C. (ed.): Speaker Classification I: Fundamentals, Features, and Methods, vol. 4343/2007. Springer: Lecture Notes in Computer Science, Berlin (2007)
Gray, R.: Vector qantization. In: IEEE ASSP Magazine, pp. 4–29 (1984)
Reynolds, D.A.: A Gaussian Mixture Modeling Approach to Text-Independent Speaker Identification. PhD thesis, Georgia Institute of Technology (1992)
Reynolds, D.A., Rose, R.C.: Robust text-independent speaker identification using Gaussian mixture speaker models. IEEE Trans. Acoust. Speech Signal Process. 3(1), 72–83 (1995)
McLachlan, G. (ed.): Mixture Models. Marcel Dekker, New York, NY (1988)
Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. J. Royal Stat. Soc. 39(1), 1–38 (1977)
Reynolds, D.A., Quatieri, T.F., Dunn, R.B.: Speaker verification using adapted Gaussian mixture models. Digital Signal Process. 10(1), 19–41 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this entry
Cite this entry
Reynolds, D. (2009). Gaussian Mixture Models. In: Li, S.Z., Jain, A. (eds) Encyclopedia of Biometrics. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-73003-5_196
Download citation
DOI: https://doi.org/10.1007/978-0-387-73003-5_196
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-73002-8
Online ISBN: 978-0-387-73003-5
eBook Packages: Computer ScienceReference Module Computer Science and Engineering