---
name: "mlpack_gmm_EMFit"
section: "3"
platform: "linux"
package: "mlpack-doc"
version: "1.0.10-1"
release: "Debian 8 (Jessie)"
platforms: ["linux"]
url: "https://new.carta.tech/mlpack_gmm_EMFit"
---

# mlpack\_gmm\_EMFit(3)

This class contains methods which can fit a GMM to observations using the EM algorithm.

## NAME

mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \> -

This class contains methods which can fit a **GMM** to observations using the EM algorithm.

## SYNOPSIS

### Public Member Functions

**EMFit** (const size\_t **maxIterations**=300, const double **tolerance**=1e-10, InitialClusteringType clusterer=InitialClusteringType(), CovarianceConstraintPolicy constraint=CovarianceConstraintPolicy())\
 *Construct the* **EMFit** *object, optionally passing an InitialClusteringType object (just in case it needs to store state).*  const InitialClusteringType & **Clusterer** () const \
 *Get the clusterer.*  InitialClusteringType & **Clusterer** ()\
 *Modify the clusterer.*  const CovarianceConstraintPolicy & **Constraint** () const \
 *Get the covariance constraint policy class.*  CovarianceConstraintPolicy & **Constraint** ()\
 *Modify the covariance constraint policy class.*  void **Estimate** (const arma::mat &observations, std::vector\< arma::vec \> &means, std::vector\< arma::mat \> &covariances, arma::vec &weights, const bool useInitialModel=false)\
 *Fit the observations to a Gaussian mixture model (***GMM***) using the EM algorithm.*  void **Estimate** (const arma::mat &observations, const arma::vec &probabilities, std::vector\< arma::vec \> &means, std::vector\< arma::mat \> &covariances, arma::vec &weights, const bool useInitialModel=false)\
 *Fit the observations to a Gaussian mixture model (***GMM***) using the EM algorithm, taking into account the probabilities of each point being from this mixture.*  size\_t **MaxIterations** () const \
 *Get the maximum number of iterations of the EM algorithm.*  size\_t & **MaxIterations** ()\
 *Modify the maximum number of iterations of the EM algorithm.*  double **Tolerance** () const \
 *Get the tolerance for the convergence of the EM algorithm.*  double & **Tolerance** ()\
 *Modify the tolerance for the convergence of the EM algorithm.*

### Private Member Functions

void **InitialClustering** (const arma::mat &observations, std::vector\< arma::vec \> &means, std::vector\< arma::mat \> &covariances, arma::vec &weights)\
 *Run the clusterer, and then turn the cluster assignments into Gaussians.*  double **LogLikelihood** (const arma::mat &data, const std::vector\< arma::vec \> &means, const std::vector\< arma::mat \> &covariances, const arma::vec &weights) const \
 *Calculate the log-likelihood of a model.*

### Private Attributes

InitialClusteringType **clusterer**\
 *Object which will perform the clustering.*  CovarianceConstraintPolicy **constraint**\
 *Object which applies constraints to the covariance matrix.*  size\_t **maxIterations**\
 *Maximum iterations of EM algorithm.*  double **tolerance**\
 *Tolerance for convergence of EM.*

## Detailed Description

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\>class mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>

This class contains methods which can fit a **GMM** to observations using the EM algorithm.

It requires an initial clustering mechanism, which is by default the KMeans algorithm. The clustering mechanism must implement the following method:

- •

  void Cluster(const arma::mat& observations, const size\_t clusters, arma::Col\<size\_t\>& assignments);

This method should create 'clusters' clusters, and return the assignment of each point to a cluster.

Definition at line 51 of file em\_fit.hpp.

## Constructor & Destructor Documentation

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::EMFit (const size\_tmaxIterations = `300`, const doubletolerance = `1e-10`, InitialClusteringTypeclusterer = `InitialClusteringType()`, CovarianceConstraintPolicyconstraint = `CovarianceConstraintPolicy()`)

Construct the **EMFit** object, optionally passing an InitialClusteringType object (just in case it needs to store state). Setting the maximum number of iterations to 0 means that the EM algorithm will iterate until convergence (with the given tolerance).

The parameter forcePositive controls whether or not the covariance matrices are checked for positive definiteness at each iteration. This could be a time-consuming task, so, if you know your data is well-behaved, you can set it to false and save some runtime.

**Parameters:**

*maxIterations* Maximum number of iterations for EM. \
 *tolerance* Log-likelihood tolerance required for convergence. \
 *forcePositive* Check for positive-definiteness of each covariance matrix at each iteration. \
 *clusterer* Object which will perform the initial clustering.

## Member Function Documentation

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> const InitialClusteringType& mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Clusterer () const` [inline]`

Get the clusterer.

Definition at line 122 of file em\_fit.hpp.

References mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::clusterer.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> InitialClusteringType& mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Clusterer ()` [inline]`

Modify the clusterer.

Definition at line 124 of file em\_fit.hpp.

References mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::clusterer.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> const CovarianceConstraintPolicy& mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Constraint () const` [inline]`

Get the covariance constraint policy class.

Definition at line 127 of file em\_fit.hpp.

References mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::constraint.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> CovarianceConstraintPolicy& mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Constraint ()` [inline]`

Modify the covariance constraint policy class.

Definition at line 129 of file em\_fit.hpp.

References mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::constraint.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> void mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Estimate (const arma::mat &observations, std::vector\< arma::vec \> &means, std::vector\< arma::mat \> &covariances, arma::vec &weights, const booluseInitialModel = `false`)

Fit the observations to a Gaussian mixture model (**GMM**) using the EM algorithm. The size of the vectors (indicating the number of components) must already be set. Optionally, if useInitialModel is set to true, then the model given in the means, covariances, and weights parameters is used as the initial model, instead of using the InitialClusteringType::Cluster() option.

**Parameters:**

*observations* List of observations to train on. \
 *means* Vector to store trained means in. \
 *covariances* Vector to store trained covariances in. \
 *weights* Vector to store a priori weights in. \
 *useInitialModel* If true, the given model is used for the initial clustering.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> void mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Estimate (const arma::mat &observations, const arma::vec &probabilities, std::vector\< arma::vec \> &means, std::vector\< arma::mat \> &covariances, arma::vec &weights, const booluseInitialModel = `false`)

Fit the observations to a Gaussian mixture model (**GMM**) using the EM algorithm, taking into account the probabilities of each point being from this mixture. The size of the vectors (indicating the number of components) must already be set. Optionally, if useInitialModel is set to true, then the model given in the means, covariances, and weights parameters is used as the initial model, instead of using the InitialClusteringType::Cluster() option.

**Parameters:**

*observations* List of observations to train on. \
 *probabilities* Probability of each point being from this model. \
 *means* Vector to store trained means in. \
 *covariances* Vector to store trained covariances in. \
 *weights* Vector to store a priori weights in. \
 *useInitialModel* If true, the given model is used for the initial clustering.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> void mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::InitialClustering (const arma::mat &observations, std::vector\< arma::vec \> &means, std::vector\< arma::mat \> &covariances, arma::vec &weights)` [private]`

Run the clusterer, and then turn the cluster assignments into Gaussians. This is a helper function for both overloads of **Estimate()**. The vectors must be already set to the number of clusters.

**Parameters:**

*observations* List of observations. \
 *means* Vector to store means in. \
 *covariances* Vector to store covariances in. \
 *weights* Vector to store a priori weights in.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> double mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::LogLikelihood (const arma::mat &data, const std::vector\< arma::vec \> &means, const std::vector\< arma::mat \> &covariances, const arma::vec &weights) const` [private]`

Calculate the log-likelihood of a model. Yes, this is reimplemented in the **GMM** code. Intuition suggests that the log-likelihood is not the best way to determine if the EM algorithm has converged.

**Parameters:**

*data* Data matrix. \
 *means* Vector of means. \
 *covariances* Vector of covariance matrices. \
 *weights* Vector of a priori weights.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> size\_t mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::MaxIterations () const` [inline]`

Get the maximum number of iterations of the EM algorithm.

Definition at line 132 of file em\_fit.hpp.

References mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::maxIterations.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> size\_t& mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::MaxIterations ()` [inline]`

Modify the maximum number of iterations of the EM algorithm.

Definition at line 134 of file em\_fit.hpp.

References mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::maxIterations.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> double mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Tolerance () const` [inline]`

Get the tolerance for the convergence of the EM algorithm.

Definition at line 137 of file em\_fit.hpp.

References mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::tolerance.

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> double& mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Tolerance ()` [inline]`

Modify the tolerance for the convergence of the EM algorithm.

Definition at line 139 of file em\_fit.hpp.

References mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::tolerance.

## Member Data Documentation

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> InitialClusteringType mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::clusterer` [private]`

Object which will perform the clustering.

Definition at line 177 of file em\_fit.hpp.

Referenced by mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Clusterer().

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> CovarianceConstraintPolicy mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::constraint` [private]`

Object which applies constraints to the covariance matrix.

Definition at line 179 of file em\_fit.hpp.

Referenced by mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Constraint().

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> size\_t mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::maxIterations` [private]`

Maximum iterations of EM algorithm.

Definition at line 173 of file em\_fit.hpp.

Referenced by mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::MaxIterations().

### template\<typename InitialClusteringType = kmeans::KMeans\<\>, typename CovarianceConstraintPolicy = PositiveDefiniteConstraint\> double mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::tolerance` [private]`

Tolerance for convergence of EM.

Definition at line 175 of file em\_fit.hpp.

Referenced by mlpack::gmm::EMFit\< InitialClusteringType, CovarianceConstraintPolicy \>::Tolerance().

## Author

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