2D Gaussian Mixture Model Expectation Maximum¶
Synopsis¶
2D Gaussian Mixture Model Expectation Maximization.
Results¶
Output:
Cluster[0]
Parameters:
[101.40933830302448, 99.43004497807948, 1098.5993639665169, -107.16526601343287, -107.16526601343287, 913.9641556669595]
Proportion: 0.495716
Cluster[1]
Parameters:
[196.3354813961237, 195.29542020949035, 991.7367739288584, 84.51759523418217, 84.51759523418217, 845.9604643808337]
Proportion: 0.504284
Code¶
C++¶
#include "itkVector.h"
#include "itkListSample.h"
#include "itkGaussianMixtureModelComponent.h"
#include "itkExpectationMaximizationMixtureModelEstimator.h"
#include "itkNormalVariateGenerator.h"
int
main(int, char *[])
{
unsigned int numberOfClasses = 2;
using MeasurementVectorType = itk::Vector<double, 2>;
using SampleType = itk::Statistics::ListSample<MeasurementVectorType>;
SampleType::Pointer sample = SampleType::New();
using NormalGeneratorType = itk::Statistics::NormalVariateGenerator;
NormalGeneratorType::Pointer normalGenerator = NormalGeneratorType::New();
// Create the first set of 2D Gaussian samples
normalGenerator->Initialize(101);
MeasurementVectorType mv;
double mean = 100;
double standardDeviation = 30;
for (unsigned int i = 0; i < 100; ++i)
{
mv[0] = (normalGenerator->GetVariate() * standardDeviation) + mean;
mv[1] = (normalGenerator->GetVariate() * standardDeviation) + mean;
sample->PushBack(mv);
}
// Create the second set of 2D Gaussian samples
normalGenerator->Initialize(3024);
mean = 200;
standardDeviation = 30;
for (unsigned int i = 0; i < 100; ++i)
{
mv[0] = (normalGenerator->GetVariate() * standardDeviation) + mean;
mv[1] = (normalGenerator->GetVariate() * standardDeviation) + mean;
sample->PushBack(mv);
}
using ParametersType = itk::Array<double>;
ParametersType params(6);
// Create the first set of initial parameters
std::vector<ParametersType> initialParameters(numberOfClasses);
params[0] = 110.0; // mean of dimension 1
params[1] = 115.0; // mean of dimension 2
params[2] = 800.0; // covariance(0,0)
params[3] = 0; // covariance(0,1)
params[4] = 0; // covariance(1,0)
params[5] = 805.0; // covariance(1,1)
initialParameters[0] = params;
// Create the second set of initial parameters
params[0] = 210.0; // mean of dimension 1
params[1] = 215.0; // mean of dimension 2
params[2] = 850.0; // covariance(0,0)
params[3] = 0; // covariance(0,1)
params[4] = 0; // covariance(1,0)
params[5] = 855.0; // covariance(1,1)
initialParameters[1] = params;
using ComponentType = itk::Statistics::GaussianMixtureModelComponent<SampleType>;
// Create the components
std::vector<ComponentType::Pointer> components;
for (unsigned int i = 0; i < numberOfClasses; i++)
{
components.push_back(ComponentType::New());
(components[i])->SetSample(sample);
(components[i])->SetParameters(initialParameters[i]);
}
using EstimatorType = itk::Statistics::ExpectationMaximizationMixtureModelEstimator<SampleType>;
EstimatorType::Pointer estimator = EstimatorType::New();
estimator->SetSample(sample);
estimator->SetMaximumIteration(200);
itk::Array<double> initialProportions(numberOfClasses);
initialProportions[0] = 0.5;
initialProportions[1] = 0.5;
estimator->SetInitialProportions(initialProportions);
for (unsigned int i = 0; i < numberOfClasses; i++)
{
estimator->AddComponent((ComponentType::Superclass *)(components[i]).GetPointer());
}
estimator->Update();
// Output the results
for (unsigned int i = 0; i < numberOfClasses; i++)
{
std::cout << "Cluster[" << i << "]" << std::endl;
std::cout << " Parameters:" << std::endl;
std::cout << " " << (components[i])->GetFullParameters() << std::endl;
std::cout << " Proportion: ";
std::cout << " " << estimator->GetProportions()[i] << std::endl;
}
return EXIT_SUCCESS;
}
Python¶
Classes demonstrated¶
Warning
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