org.openimaj.math.statistics.distribution

Class MixtureOfGaussians

java.lang.Object

org.openimaj.math.statistics.distribution.AbstractMultivariateDistribution

org.openimaj.math.statistics.distribution.MixtureOfGaussians

All Implemented Interfaces:

MultivariateDistribution

Direct Known Subclasses:

GaussianMixtureModelEM.EMGMM

public class MixtureOfGaussians
extends AbstractMultivariateDistribution

Implementation of a mixture of gaussians (gaussian mixture model). This class only models the distribution itself, and does not contain the necessary code to learn a mixture (for that see the GaussianMixtureModelEM class for example).

Author:

Jonathon Hare (jsh2@ecs.soton.ac.uk)

Field Summary

Fields

Modifier and Type	Field and Description
MultivariateGaussian[]	gaussians The individual gaussians
static double	MIN_COVAR_RECONDITION Amount to add to the diagonal of the covariance matrix if it's ill-conditioned.
double[]	weights The weight of each gaussian

Constructor Summary

Constructors

Constructor and Description
MixtureOfGaussians(MultivariateGaussian[] gaussians, double[] weights) Construct the mixture with the given gaussians and weights

Method Summary

Modifier and Type	Method and Description
protected double[][]	computeWeightedLogProb(double[][] samples)
double	estimateLogProbability(double[] sample) Get the log probability for a given point in space relative to the PDF represented by this distribution.
double[]	estimateLogProbability(double[][] samples) Get the probability for a given points in space relative to the PDF represented by the gaussian mixture.
double	estimateProbability(double[] sample) Get the probability for a given point in space relative to the PDF represented by this distribution.
MultivariateGaussian[]	getGaussians() Get the gaussians that make up the mixture
double[]	getWeights() Get the mixture weights for each gaussian.
double[][]	logProbability(double[][] x) Compute the log probability of the given data points belonging to each of the gaussians
static double[][]	logProbability(double[][] x, MultivariateGaussian[] gaussians) Compute the log probability of the given data points belonging to each of the given gaussians
int	predict(double[] data) Predict the class (the index of the most-probable gaussian) to which the given data point belongs.
double[]	predictLogPosterior(double[] sample) Predict the log-posterior for the given sample; this is the log-probability of the sample point belonging to each of the gaussians in the mixture.
double[][]	predictLogPosterior(double[][] samples) Predict the log-posterior for the given samples; this is the log-probability of each sample point belonging to each of the gaussians in the mixture.
double[][]	sample(int n_samples, Random rng) Sample the distribution.
double[]	sample(Random rng) Sample the distribution.
IndependentPair<double[],double[][]>	scoreSamples(double[][] samples) Compute the posterior distribution of the samples, and the overall log probability of each sample as belonging to the model.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

MIN_COVAR_RECONDITION

public static final double MIN_COVAR_RECONDITION

Amount to add to the diagonal of the covariance matrix if it's ill-conditioned.

See Also:

Constant Field Values

gaussians

public MultivariateGaussian[] gaussians

The individual gaussians

weights

public double[] weights

The weight of each gaussian

Constructor Detail

MixtureOfGaussians

public MixtureOfGaussians(MultivariateGaussian[] gaussians,
                          double[] weights)

Construct the mixture with the given gaussians and weights

Parameters:

gaussians - the gaussians

weights - the weights

Method Detail

sample

public double[] sample(Random rng)

Description copied from interface: MultivariateDistribution

Sample the distribution. the number of samples to draw

Parameters:

rng - the random number generator

Returns:

a list of sample vectors from this distribution

sample

public double[][] sample(int n_samples,
                         Random rng)

Description copied from interface: MultivariateDistribution

Sample the distribution.

Specified by:

sample in interface MultivariateDistribution

Overrides:

sample in class AbstractMultivariateDistribution

Parameters:

n_samples - the number of samples to draw

rng - the random number generator

Returns:

a list of sample vectors from this distribution

estimateLogProbability

public double estimateLogProbability(double[] sample)

Description copied from interface: MultivariateDistribution

Get the log probability for a given point in space relative to the PDF represented by this distribution.

Specified by:

estimateLogProbability in interface MultivariateDistribution

Overrides:

estimateLogProbability in class AbstractMultivariateDistribution

Parameters:

sample - the point

Returns:

the log-probability

estimateLogProbability

public double[] estimateLogProbability(double[][] samples)

Get the probability for a given points in space relative to the PDF represented by the gaussian mixture.

Parameters:

samples - the points

Returns:

the probability

logProbability

public static double[][] logProbability(double[][] x,
                                        MultivariateGaussian[] gaussians)

Compute the log probability of the given data points belonging to each of the given gaussians

Parameters:

x - the points

gaussians - the gaussians

Returns:

the log probability of each point belonging to each gaussian distribution

computeWeightedLogProb

protected double[][] computeWeightedLogProb(double[][] samples)

logProbability

public double[][] logProbability(double[][] x)

Compute the log probability of the given data points belonging to each of the gaussians

Parameters:

x - the points

Returns:

the log probability of each point belonging to each gaussian distribution

predictLogPosterior

public double[] predictLogPosterior(double[] sample)

Predict the log-posterior for the given sample; this is the log-probability of the sample point belonging to each of the gaussians in the mixture.

Parameters:

sample - the sample

Returns:

the log-probability for each gaussian

predictLogPosterior

public double[][] predictLogPosterior(double[][] samples)

Predict the log-posterior for the given samples; this is the log-probability of each sample point belonging to each of the gaussians in the mixture.

Parameters:

samples - the samples

Returns:

the log-probability for each gaussian

scoreSamples

public IndependentPair<double[],double[][]> scoreSamples(double[][] samples)

Compute the posterior distribution of the samples, and the overall log probability of each sample as belonging to the model.

Parameters:

samples - the samples

Returns:

a pair of (log probabilities, log posterior probabilities)

getGaussians

public MultivariateGaussian[] getGaussians()

Get the gaussians that make up the mixture

Returns:

the gaussians

getWeights

public double[] getWeights()

Get the mixture weights for each gaussian.

Returns:

the weights

estimateProbability

public double estimateProbability(double[] sample)

Description copied from interface: MultivariateDistribution

Get the probability for a given point in space relative to the PDF represented by this distribution.

Parameters:

sample - the point

Returns:

the probability

predict

public int predict(double[] data)

Predict the class (the index of the most-probable gaussian) to which the given data point belongs.

Parameters:

data - the data point

Returns:

the class index