R: Modal EM algorithm for Gaussian Mixtures

GaussianMixtureMEM {mclustAddons}

R Documentation

Modal EM algorithm for Gaussian Mixtures

Description

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

Usage

GaussianMixtureMEM(data, pro, mu, sigma,
                   control = list(eps = 1e-5, 
                                  maxiter = 1e3, 
                                  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.

Author(s)

Luca Scrucca

References

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