A Gaussian mixture model is a mixture distribution whose component distributions are normal distributions. Its probability density function has the form
 |
where 
,
,
and 
is the probability density function
of a multivariate normal distribution
with mean 
and covariance matrix 
.
The component label is an unobserved categorical random variable. Model parameters are often estimated by alternately estimating component memberships and maximizing the resulting expected log likelihood function. A Gaussian mixture can be unimodal or multimodal, depending on its weights, means, and covariance matrices.
