ml_gaussian_mixture

ml_gaussian_mixture(
    x,
    k,
    seed=None,
    kmeans_plus_plus=True,
    max_iterations=1000,
    tolerance=1e-08,
)

Gaussian mixture model.

Mirrors the C# GaussianMixtureModel class: fits a mixture of k multivariate normals by expectation-maximization, initialized from a k-means fit. It generalizes :func:ml_kmeans by carrying a full covariance per component rather than only a centre.

labels are 0-BASED, as in :func:ml_kmeans. log_likelihood follows the library’s own definition, which OMITS the multivariate-normal normalizing constant -0.5 * x.shape[1] * log(2 * pi) per observation – so it is short of the true mixture log-likelihood by x.shape[0] * x.shape[1] / 2 * log(2 * pi). That constant cancels when comparing two fits of the same data (which is what the library uses it for), but do not feed this value to an information criterion without adding it back. A run that hits max_iterations without converging reports log_likelihood as 0.

Parameters

Name	Type	Description	Default
x	array_like	A 2-D array with one row per observation, or a 1-D array.	required
k	int	The number of mixture components.	required
seed	int	PRNG seed; None uses the computer clock.	None
kmeans_plus_plus	bool	Use k-means++ initialization for the starting fit.	True
max_iterations	int	The EM iteration cap.	1000
tolerance	float	The relative convergence tolerance on the log-likelihood.	1e-8

Returns

Name	Type	Description
	dict	means (k by p), sigmas (a length-k list of p-by-p covariance arrays), weights, labels (0-based), log_likelihood, and iterations.

Examples

>>> from corehydropy import ml_gaussian_mixture
>>> x = [1, 1.2, 0.9, 1.1, 1.05, 8, 8.3, 7.9, 8.1, 8.2, 1.0, 8.0]
>>> fit = ml_gaussian_mixture(x, k=2, seed=12345)
>>> len(fit["sigmas"])
2