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# Gaussian Mixture#

A Gaussian Mixture model (GMM) is a probabilistic model for representing the presence of clusters within an overall population without requiring a sample to know which sub-population it belongs to beforehand. GMMs are similar to centroid-based clusterers like K Means but allow both the cluster centers (means) as well as the radii (variances) to be learned as well. For this reason, GMMs are especially useful for clusterings that are of different radii.

Interfaces: Estimator, Learner, Probabilistic, Verbose, Persistable

Data Type Compatibility: Continuous

## Parameters#

# Param Default Type Description
1 k int The number of target clusters.
2 epochs 100 int The maximum number of training rounds to execute.
3 min change 1e-3 float The minimum change in the components necessary for the algorithm to continue training.
6 seeder PlusPlus Seeder The seeder used to initialize the Gaussian components.

## Example#

``````use Rubix\ML\Clusterers\GaussianMixture;
use Rubix\ML\Clusterers\Seeders\KMC2;

\$estimator = new GaussianMixture(5, 1e-4, 100, new KMC2(50));
``````

Return the cluster prior probabilities based on their representation over all training samples:

``````public priors() : float[]
``````

Return the running means of each feature column for each cluster:

``````public means() : array[]
``````

Return the variance of each feature column for each cluster:

``````public variances() : array[]
``````

Return the loss at each epoch from the last training session:

``````public steps() : float[]|null
``````

### References#

• A. P. Dempster et al. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm.
• J. Blomer et al. (2016). Simple Methods for Initializing the EM Algorithm for Gaussian Mixture Models.