What is gaussian mixture model ?
Gaussian mixture models are a probabilistic model for representing normally distributed subpopulations within an overall population.
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The model is parameterized by two types of values:
- the mixture component weights
- the component means and variances.
For a Gaussian mixture model with components.
where and is the mean and variance to the components, and is the correspoing component weight. from the last equation we get the total probability distribution normalizes to 1.
clustering with Gaussian mixture models
we assume that the data points are gaussian distributed, each gaussian distribution is assigned to a single cluster.
we often use Expectation-Maximization(EM) to find the parameters of the Gaussian model for each cluster.
References
https://people.csail.mit.edu/rameshvs/content/gmm-em.pdf
https://brilliant.org/wiki/gaussian-mixture-model/