Modes of a Gaussian mixture

Returns the distinct local modes of a Gaussian-mixture density by Gaussian mean-shift (the fixed-point hill-climb of Carreira-Perpinan 2000) started from each component mean, together with the mixture density at each mode. Nearby converged points are merged so that each genuine mode is reported once.

Usage

gmm_modes(object, starts = NULL, tol = 1e-05, dedup = NULL, max_iter = 200L)

Arguments

object

A gmm or gmm_fit.

starts

Optional m-by-p matrix of starting points for the mean-shift. Default NULL uses the component means.

tol

Convergence tolerance on the mean-shift step length. Default 1e-5.

dedup

Distance below which two converged points are treated as the same mode. Default NULL derives a small fraction of the spread of the component means.

max_iter

Maximum mean-shift iterations per start. Default 200L.

Value

A list with modes (an n-by-p matrix of distinct modes, ordered by descending mixture density), density (the mixture density at each mode), and n (the number of modes).

Details

A mixture of K components has at most K modes, and fewer when components overlap; mean-shift from every component mean finds them robustly without a grid. The companion of from_objective(): applied to the fitted map it returns the recovered optima (ordered by density, which for a Gibbs proxy ranks the deepest optima first).

See also

from_objective(), whose fitted map this resolves into optima.

Other ops: dgmm(), gmm_canonicalise(), gmm_conditionalise(), gmm_divergence(), gmm_kld(), gmm_marginalise(), gmm_mean(), pgmm(), rgmm()

Examples

g <- gmm(
  weights = rep(1 / 3, 3),
  means = list(c(-3, 0), c(3, 0), c(0, 4)),
  covariances = rep(list(0.3 * diag(2)), 3)
)
gmm_modes(g)$modes
#>      [,1]         [,2]
#> [1,]   -3 3.209642e-18
#> [2,]    3 3.209642e-18
#> [3,]    0 4.000000e+00