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Modal EM algorithm for Gaussian Mixtures

GaussianMixtureMEM.Rd

A function implementing a fast and efficient Modal EM algorithm for Gaussian mixtures.

Usage

GaussianMixtureMEM(
  data,
  pro,
  mu,
  sigma,
  control = list(eps = 0.00001, maxiter = 1000, stepsize = function(t) 1 - exp(-0.1 * t),
    denoise = TRUE, alpha = 0.01, keep.path = FALSE),
  ...
)

Arguments

data

A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations (\(n\)) and columns correspond to variables (\(d\)).

pro

A \((G \times 1)\) vector of mixing probabilities for a Gaussian mixture of \(G\) components.

mu

A \((d \times G)\) matrix of component means for a \(d\)-variate Gaussian mixture of \(G\) components.

sigma

A \((d \times d \times G)\) array of component covariance matrices for a \(d\)-variate Gaussian mixture of \(G\) components.

control

A list of control parameters:

  • eps, maxiter Numerical values setting the tolerance and the maximum number of iterations of the MEM algorithm;

  • stepsize A function controlling the step size of the MEM algorithm;

  • denoise A logical, if TRUE a denoising procedure is used when \(d > 1\) to discard all modes whose density is negligible;

  • alpha A numerical value used when denoise = TRUE for computing the hypervolume of central \((1-\alpha)100\) region of a multivariate Gaussian;

  • keep.path A logical controlling whether or not the full paths to modes must be returned.

...

Further arguments passed to or from other methods.

Value

Returns a list containing the following elements:

  • n The number of input data points.

  • d The number of variables/features.

  • parameters The Gaussian mixture parameters.

  • iter The number of iterations of MEM algorithm.

  • nmodes The number of modes estimated by the MEM algorithm.

  • modes The coordinates of modes estimated by MEM algorithm.

  • path If requested, the coordinates of full paths to modes for each data point.

  • logdens The log-density at the estimated modes.

  • logvol The log-volume used for denoising (if requested).

  • classification The modal clustering classification of input data points.

References

Scrucca L. (2021) A fast and efficient Modal EM algorithm for Gaussian mixtures. Statistical Analysis and Data Mining, 14:4, 305–314. doi: 10.1002/sam.11527

See also

MclustMEM().

Author

Luca Scrucca