A Gaussian mixture is a probability density function (p.d.f.). It is a combination of several Gaussian densities.

The GaussianMixture's p.d.f. is defined as the weighted sum of K multivariate Gaussian p.d.f's:

pdf(x) = Σi=1K pi N(xii),

where each N(xii) is a multivariate p.d.f. with mean μi and covariance matrix Σi. The coefficients pi sum to 1.

For an introduction to Gaussian mixtures see for example Bishop (2006).

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© djmw, October 26, 2010