private UnivariateContinuousDistribution GetDistribution(double [] samples)
{
if (samples.Length < 10)
{
return(new EmpiricalDistribution(samples));
}
else
{
Accord.Math.Random.Generator.Seed = 0;
// determining the optimal number of clusters is not easy, we use
// a simple heuristics based on the numeber of samples
var clusterCount = (int)Math.Ceiling(Math.Log(samples.Length, 10));
var kmean = new KMeans(clusterCount);
var clusters = kmean.Learn(samples.Select(x => new double[] { x }).ToArray());
var components = new NormalDistribution[clusters.Count];
for (int i = 0; i < clusters.Count; i++)
{
var cluster = clusters[i];
components[i] = new NormalDistribution(cluster.Centroid.First()); //, cluster.Proportion);
}
var mix = new Mixture <NormalDistribution>(components);
mix.Fit(samples);
return(mix);
}
}
/// <summary>
/// Divides the input data into K clusters modeling each
/// cluster as a multivariate Gaussian distribution.
/// </summary>
public double Compute(double[][] data, GaussianMixtureModelOptions options)
{
if (data == null)
{
throw new ArgumentNullException("data");
}
int components = this.clusters.Count;
if (model == null)
{
// TODO: Perform K-Means multiple times to avoid
// a poor Gaussian Mixture model initialization.
double error = Initialize(data, options.Threshold);
}
// Fit a multivariate Gaussian distribution
var mixtureOptions = new MixtureOptions()
{
Threshold = options.Threshold,
InnerOptions = options.NormalOptions,
};
model.Fit(data, mixtureOptions);
// Return the log-likelihood as a measure of goodness-of-fit
return(model.LogLikelihood(data));
}
public void MixtureWeightsFitTest()
{
// Randomly initialize some mixture components
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
// Create an initial mixture
Mixture <NormalDistribution> mixture = new Mixture <NormalDistribution>(components);
// Now, suppose we have a weighted data set. Those will be the input points:
double[] points = { 0, 3, 1, 7, 3, 5, 1, 2, -1, 2, 7, 6, 8, 6 }; // (14 points)
// And those are their respective unnormalized weights:
double[] weights = { 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 3, 1, 1 }; // (14 weights)
// Let's normalize the weights so they sum up to one:
weights = weights.Divide(weights.Sum());
// Now we can fit our model to the data:
mixture.Fit(points, weights); // done!
// Our model will be:
double mean1 = mixture.Components[0].Mean; // 1.41126
double mean2 = mixture.Components[1].Mean; // 6.53301
// With mixture coefficients
double pi1 = mixture.Coefficients[0]; // 0.51408489193241225
double pi2 = mixture.Coefficients[1]; // 0.48591510806758775
Assert.AreEqual(1.4112610766836411, mean1);
Assert.AreEqual(6.5330177004151064, mean2);
Assert.AreEqual(0.51408489193241225, pi1);
Assert.AreEqual(0.48591510806758775, pi2);
/*
* // If we need the GaussianMixtureModel functionality, we can
* // use the estimated mixture to initialize a new model:
* GaussianMixtureModel gmm = new GaussianMixtureModel(mixture);
*
* Assert.AreEqual(mean1, gmm.Gaussians[0].Mean[0]);
* Assert.AreEqual(mean2, gmm.Gaussians[1].Mean[0]);
*
* Assert.AreEqual(mean1, 1.4112610766836404, 1e-15);
* Assert.AreEqual(mean2, 6.5330177004151082, 1e-14);
*
* Assert.AreEqual(mixture.Coefficients[0], gmm.Gaussians[0].Proportion);
* Assert.AreEqual(mixture.Coefficients[1], gmm.Gaussians[1].Proportion);
*/
}
public void FitTest()
{
double[] coefficients = { 0.50, 0.50 };
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
var target = new Mixture <NormalDistribution>(coefficients, components);
double[] values = { 0, 1, 1, 0, 1, 6, 6, 5, 7, 5 };
double[] part1 = values.Submatrix(0, 4);
double[] part2 = values.Submatrix(5, 9);
MixtureOptions options = new MixtureOptions()
{
Threshold = 1e-10
};
target.Fit(values, options);
var actual = target;
var mean1 = Accord.Statistics.Tools.Mean(part1);
var var1 = Accord.Statistics.Tools.Variance(part1);
Assert.AreEqual(mean1, actual.Components[0].Mean, 1e-6);
Assert.AreEqual(var1, actual.Components[0].Variance, 1e-6);
var mean2 = Accord.Statistics.Tools.Mean(part2);
var var2 = Accord.Statistics.Tools.Variance(part2);
Assert.AreEqual(mean2, actual.Components[1].Mean, 1e-6);
Assert.AreEqual(var2, actual.Components[1].Variance, 1e-5);
var expectedMean = Accord.Statistics.Tools.Mean(values);
var actualMean = actual.Mean;
Assert.AreEqual(expectedMean, actualMean, 1e-7);
var expectedVar = Accord.Statistics.Tools.Variance(values, false);
var actualVar = actual.Variance;
Assert.AreEqual(expectedVar, actualVar, 0.15);
}
public void FitTest2()
{
double[] coefficients = { 0.50, 0.50 };
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
var target = new Mixture <NormalDistribution>(coefficients, components);
double[] values = { 12512, 1, 1, 0, 1, 6, 6, 5, 7, 5 };
double[] weights = { 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
weights = weights.Divide(weights.Sum());
double[] part1 = values.Submatrix(1, 4);
double[] part2 = values.Submatrix(5, 9);
MixtureOptions opt = new MixtureOptions()
{
Threshold = 0.000001
};
target.Fit(values, weights, opt);
var mean1 = Accord.Statistics.Tools.Mean(part1);
var var1 = Accord.Statistics.Tools.Variance(part1);
Assert.AreEqual(mean1, target.Components[0].Mean, 1e-5);
Assert.AreEqual(var1, target.Components[0].Variance, 1e-5);
var mean2 = Accord.Statistics.Tools.Mean(part2);
var var2 = Accord.Statistics.Tools.Variance(part2);
Assert.AreEqual(mean2, target.Components[1].Mean, 1e-5);
Assert.AreEqual(var2, target.Components[1].Variance, 1e-5);
var expectedMean = Accord.Statistics.Tools.WeightedMean(values, weights);
var actualMean = target.Mean;
Assert.AreEqual(expectedMean, actualMean, 1e-5);
}
public void MixtureDistributionExample()
{
var samples1 = new NormalDistribution(mean: -2, stdDev: 1).Generate(10000000);
var samples2 = new NormalDistribution(mean: +4, stdDev: 1).Generate(10000000);
// Mix the samples from both distributions
var samples = samples1.Concatenate(samples2);
// Create a new mixture distribution with two Normal components
var mixture = new Mixture <NormalDistribution>(
new NormalDistribution(-1),
new NormalDistribution(+1));
// Estimate the distribution
mixture.Fit(samples);
var a = mixture.Components[0].ToString("N2"); // N(x; μ = -2.00, σ² = 1.00)
var b = mixture.Components[1].ToString("N2"); // N(x; μ = 4.00, σ² = 1.02)
Assert.AreEqual("N(x; μ = -2.00, σ² = 0.99)", a);
Assert.AreEqual("N(x; μ = 4.00, σ² = 1.01)", b);
}
public void MixtureFitTest()
{
var samples1 = new NormalDistribution(mean: -2, stdDev: 0.5).Generate(100000);
var samples2 = new NormalDistribution(mean: +4, stdDev: 0.5).Generate(100000);
// Mix the samples from both distributions
var samples = samples1.Concatenate(samples2);
// Create a new mixture distribution with two Normal components
var mixture = new Mixture <NormalDistribution>(new[] { 0.2, 0.8 },
new NormalDistribution(-1),
new NormalDistribution(+1));
// Estimate the distribution
mixture.Fit(samples, new MixtureOptions
{
Iterations = 50,
Threshold = 0
});
var result = mixture.ToString("N2", System.Globalization.CultureInfo.InvariantCulture);
Assert.AreEqual("Mixture(x; 0.50*N(x; μ = -2.00, σ² = 0.25) + 0.50*N(x; μ = 4.00, σ² = 0.25))", result);
}
public void MixtureWeightsFitTest()
{
// Randomly initialize some mixture components
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
// Create an initial mixture
Mixture<NormalDistribution> mixture = new Mixture<NormalDistribution>(components);
// Now, suppose we have a weighted data
// set. Those will be the input points:
double[] points = { 0, 3, 1, 7, 3, 5, 1, 2, -1, 2, 7, 6, 8, 6 }; // (14 points)
// And those are their respective unormalized weights:
double[] weights = { 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 3, 1, 1 }; // (14 weights)
// Let's normalize the weights so they sum up to one:
weights = weights.Divide(weights.Sum());
// Now we can fit our model to the data:
mixture.Fit(points, weights); // done!
// Our model will be:
double mean1 = mixture.Components[0].Mean; // 1.41126
double mean2 = mixture.Components[1].Mean; // 6.53301
// If we need the GaussianMixtureModel functionality, we can
// use the estimated mixture to initialize a new model:
GaussianMixtureModel gmm = new GaussianMixtureModel(mixture);
Assert.AreEqual(mean1, gmm.Gaussians[0].Mean[0]);
Assert.AreEqual(mean2, gmm.Gaussians[1].Mean[0]);
Assert.AreEqual(mean1, 1.4112610766836404, 1e-15);
Assert.AreEqual(mean2, 6.5330177004151082, 1e-14);
Assert.AreEqual(mixture.Coefficients[0], gmm.Gaussians[0].Proportion);
Assert.AreEqual(mixture.Coefficients[1], gmm.Gaussians[1].Proportion);
}
public void FitTest2()
{
double[] coefficients = { 0.50, 0.50 };
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
var target = new Mixture<NormalDistribution>(coefficients, components);
double[] values = { 12512, 1, 1, 0, 1, 6, 6, 5, 7, 5 };
double[] weights = { 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
weights = weights.Divide(weights.Sum());
double[] part1 = values.Submatrix(1, 4);
double[] part2 = values.Submatrix(5, 9);
MixtureOptions opt = new MixtureOptions()
{
Threshold = 0.000001
};
target.Fit(values, weights, opt);
var mean1 = Accord.Statistics.Tools.Mean(part1);
var var1 = Accord.Statistics.Tools.Variance(part1);
Assert.AreEqual(mean1, target.Components[0].Mean, 1e-5);
Assert.AreEqual(var1, target.Components[0].Variance, 1e-5);
var mean2 = Accord.Statistics.Tools.Mean(part2);
var var2 = Accord.Statistics.Tools.Variance(part2);
Assert.AreEqual(mean2, target.Components[1].Mean, 1e-5);
Assert.AreEqual(var2, target.Components[1].Variance, 1e-5);
var expectedMean = Accord.Statistics.Tools.WeightedMean(values, weights);
var actualMean = target.Mean;
Assert.AreEqual(expectedMean, actualMean, 1e-5);
}
public void FitTest()
{
double[] coefficients = { 0.50, 0.50 };
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
var target = new Mixture<NormalDistribution>(coefficients, components);
double[] values = { 0, 1, 1, 0, 1, 6, 6, 5, 7, 5 };
double[] part1 = values.Submatrix(0, 4);
double[] part2 = values.Submatrix(5, 9);
MixtureOptions options = new MixtureOptions() { Threshold = 1e-10 };
target.Fit(values, options);
var actual = target;
var mean1 = Accord.Statistics.Tools.Mean(part1);
var var1 = Accord.Statistics.Tools.Variance(part1);
Assert.AreEqual(mean1, actual.Components[0].Mean, 1e-6);
Assert.AreEqual(var1, actual.Components[0].Variance, 1e-6);
var mean2 = Accord.Statistics.Tools.Mean(part2);
var var2 = Accord.Statistics.Tools.Variance(part2);
Assert.AreEqual(mean2, actual.Components[1].Mean, 1e-6);
Assert.AreEqual(var2, actual.Components[1].Variance, 1e-5);
var expectedMean = Accord.Statistics.Tools.Mean(values);
var actualMean = actual.Mean;
Assert.AreEqual(expectedMean, actualMean, 1e-7);
var expectedVar = Accord.Statistics.Tools.Variance(values, false);
var actualVar = actual.Variance;
Assert.AreEqual(expectedVar, actualVar, 0.15);
}
public void MixtureDistributionExample()
{
var samples1 = new NormalDistribution(mean: -2, stdDev: 1).Generate(100000);
var samples2 = new NormalDistribution(mean: +4, stdDev: 1).Generate(100000);
// Mix the samples from both distributions
var samples = samples1.Concatenate(samples2);
// Create a new mixture distribution with two Normal components
var mixture = new Mixture<NormalDistribution>(
new NormalDistribution(-1),
new NormalDistribution(+1));
// Estimate the distribution
mixture.Fit(samples);
var a = mixture.Components[0].ToString("N2"); // N(x; μ = -2.00, σ² = 1.00)
var b = mixture.Components[1].ToString("N2"); // N(x; μ = 4.00, σ² = 1.02)
Assert.AreEqual("N(x; μ = -2.00, σ² = 1.00)", a);
Assert.AreEqual("N(x; μ = 4.00, σ² = 1.02)", b);
}
public void MixtureFitTest()
{
var samples1 = new NormalDistribution(mean: -2, stdDev: 0.5).Generate(100000);
var samples2 = new NormalDistribution(mean: +4, stdDev: 0.5).Generate(100000);
// Mix the samples from both distributions
var samples = samples1.Concatenate(samples2);
// Create a new mixture distribution with two Normal components
var mixture = new Mixture<NormalDistribution>(new[] { 0.2, 0.8 },
new NormalDistribution(-1),
new NormalDistribution(+1));
// Estimate the distribution
mixture.Fit(samples, new MixtureOptions
{
Iterations = 50,
Threshold = 0
});
var result = mixture.ToString("N2", System.Globalization.CultureInfo.InvariantCulture);
Assert.AreEqual("Mixture(x; 0.50*N(x; μ = -2.00, σ² = 0.25) + 0.50*N(x; μ = 4.00, σ² = 0.25))", result);
}