MultivariateNormalMixtureExpectationMaximization (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.distribution.fitting.MultivariateNormalMixtureExpectationMaximization

```
public class MultivariateNormalMixtureExpectationMaximization
extends Object
```
Expectation-Maximization algorithm for fitting the parameters of multivariate normal mixture model distributions. This implementation is pure original code based on EM Demystified: An Expectation-Maximization Tutorial by Yihua Chen and Maya R. Gupta, Department of Electrical Engineering, University of Washington, Seattle, WA 98195. It was verified using external tools like CRAN Mixtools (see the JUnit test cases) but it is not based on Mixtools code at all. The discussion of the origin of this class can be seen in the comments of the MATH-817 JIRA issue.

Since:

3.2

Constructor Summary

Constructors
Constructor and Description

MultivariateNormalMixtureExpectationMaximization(double[][] data)
Creates an object to fit a multivariate normal mixture model to data.

Constructors
Constructor and Description
`MultivariateNormalMixtureExpectationMaximization(double[][] data)` Creates an object to fit a multivariate normal mixture model to data.

Method Summary

Methods
Modifier and Type	Method and Description
`static MixtureMultivariateNormalDistribution`	`estimate(double[][] data, int numComponents)` Helper method to create a multivariate normal mixture model which can be used to initialize `fit(MixtureMultivariateNormalDistribution)`.
`void`	`fit(MixtureMultivariateNormalDistribution initialMixture)` Fit a mixture model to the data supplied to the constructor.
`void`	`fit(MixtureMultivariateNormalDistribution initialMixture, int maxIterations, double threshold)` Fit a mixture model to the data supplied to the constructor.
`MixtureMultivariateNormalDistribution`	`getFittedModel()` Gets the fitted model.
`double`	`getLogLikelihood()` Gets the log likelihood of the data under the fitted model.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - MultivariateNormalMixtureExpectationMaximization
```
public MultivariateNormalMixtureExpectationMaximization(double[][] data)
                                                 throws NotStrictlyPositiveException,
                                                        DimensionMismatchException,
                                                        NumberIsTooSmallException
```
    Creates an object to fit a multivariate normal mixture model to data.
    
    Parameters:
    data - Data to use in fitting procedure
    
    Throws:
    
    NotStrictlyPositiveException - if data has no rows
    
    DimensionMismatchException - if rows of data have different numbers of columns
    
    NumberIsTooSmallException - if the number of columns in the data is less than 2
- Method Detail
  - fit
```
public void fit(MixtureMultivariateNormalDistribution initialMixture,
       int maxIterations,
       double threshold)
         throws SingularMatrixException,
                NotStrictlyPositiveException,
                DimensionMismatchException
```
    Fit a mixture model to the data supplied to the constructor. The quality of the fit depends on the concavity of the data provided to the constructor and the initial mixture provided to this function. If the data has many local optima, multiple runs of the fitting function with different initial mixtures may be required to find the optimal solution. If a SingularMatrixException is encountered, it is possible that another initialization would work.
    
    Parameters:
    initialMixture - Model containing initial values of weights and multivariate normals
    maxIterations - Maximum iterations allowed for fit
    threshold - Convergence threshold computed as difference in logLikelihoods between successive iterations
    
    Throws:
    
    SingularMatrixException - if any component's covariance matrix is singular during fitting
    
    NotStrictlyPositiveException - if numComponents is less than one or threshold is less than Double.MIN_VALUE
    
    DimensionMismatchException - if initialMixture mean vector and data number of columns are not equal
  - fit
```
public void fit(MixtureMultivariateNormalDistribution initialMixture)
         throws SingularMatrixException,
                NotStrictlyPositiveException
```
    Fit a mixture model to the data supplied to the constructor. The quality of the fit depends on the concavity of the data provided to the constructor and the initial mixture provided to this function. If the data has many local optima, multiple runs of the fitting function with different initial mixtures may be required to find the optimal solution. If a SingularMatrixException is encountered, it is possible that another initialization would work.
    
    Parameters:
    initialMixture - Model containing initial values of weights and multivariate normals
    
    Throws:
    
    SingularMatrixException - if any component's covariance matrix is singular during fitting
    
    NotStrictlyPositiveException - if numComponents is less than one or threshold is less than Double.MIN_VALUE
  - estimate
```
public static MixtureMultivariateNormalDistribution estimate(double[][] data,
                                             int numComponents)
                                                      throws NotStrictlyPositiveException,
                                                             DimensionMismatchException
```
    Helper method to create a multivariate normal mixture model which can be used to initialize fit(MixtureMultivariateNormalDistribution). This method uses the data supplied to the constructor to try to determine a good mixture model at which to start the fit, but it is not guaranteed to supply a model which will find the optimal solution or even converge.
    
    Parameters:
    data - Data to estimate distribution
    numComponents - Number of components for estimated mixture
    
    Returns:
    Multivariate normal mixture model estimated from the data
    
    Throws:
    
    NumberIsTooLargeException - if numComponents is greater than the number of data rows.
    
    NumberIsTooSmallException - if numComponents < 2.
    
    NotStrictlyPositiveException - if data has less than 2 rows
    
    DimensionMismatchException - if rows of data have different numbers of columns
  - getLogLikelihood
```
public double getLogLikelihood()
```
    Gets the log likelihood of the data under the fitted model.
    
    Returns:
    Log likelihood of data or zero of no data has been fit
  - getFittedModel
```
public MixtureMultivariateNormalDistribution getFittedModel()
```
    Gets the fitted model.
    
    Returns:
    fitted model or null if no fit has been performed yet.

Class MultivariateNormalMixtureExpectationMaximization

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MultivariateNormalMixtureExpectationMaximization

Method Detail

fit

fit

estimate

getLogLikelihood

getFittedModel