Gaussian Mixture Function

A Gaussian Mixture Function is a mixture density function composed of two or more Gaussian density functions.

• Context:
  • It can be a member of a Gaussian Mixture Model Family.
  • It can range from being a Finite Gaussian Mixture Function (e.g. a 2-component Gaussian mixture) to being an Infinite Gaussian Mixture Function.
  • It can range from being a Univariate Gaussian Mixture Function to being a Multivariate Gaussian Mixture Function.
  • …
• Example(s):
  • a Univariate Two-Component Gaussian: .
  • a Univariate Three-Component Gaussian: ,
  • a Bivariate Two-Component Gaussian:
• Counter-Example(s):
  • a Radial Distribution Function.
  • a Poisson Mixture Function.
  • a Heterogeneous Mixture Function.
  • a One-Component Gaussian Function.
• See: Gaussian Process Neural Net, Gaussian Random Field, Finite Mixture Function, Vector Space.

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References

2010

• http://www.mathworks.com/matlabcentral/fileexchange/24867-gaussianmixturemodel-m/content/gaussian_mixture_model.m
  • A Gaussian mixture model means that each data point is drawn (randomly) from one of C classes of data, with probability p_i of being drawn from class i, and each class is distributed as a Gaussian with mean standard deviation mu_i and sigma_i. Given a set of data drawn from such a distribution, we seek to estimate these unknown parameters.

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