org.apache.commons.math3.distribution.fitting

## Class MultivariateNormalMixtureExpectationMaximization

- 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.

  - ### 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.

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