/// <summary>
/// Calcualtes loglikelihood of Gaussian Mixture Distribution
/// </summary>
/// <param name="observations">Observation seuqnce</param>
/// <param name="mixingCoefficients">Mixing coeficients</param>
/// <param name="covariances">Array of covariance matrixes</param>
/// <param name="mean">Array of mean vectors</param>
/// <returns>Loglikelihood</returns>
public static double Calculate(double[][] observations, double[] mixingCoefficients, double[][,] covariances, double[][] means)
{
var N = observations.Length;
var K = mixingCoefficients.Length;
var D = means[0].Length;
var result = 0.0d;
var constant = (1 / Math.Pow(Math.Sqrt(2 * Math.PI), D));
for (int n = 0; n < N; n++)
{
var x = observations[n];
var mixtureResult = 0.0;
for (int k = 0; k < K; k++)
{
var covarianceMatrix = new Matrix(covariances[k]);
var covarianceMatrixInverse = covarianceMatrix.Inverse();
var distance = Mahalanobis.Calculate(x, means[k], covarianceMatrixInverse);
var prefix = constant * (1 / Math.Sqrt(covarianceMatrix.Determinant));
mixtureResult += mixingCoefficients[k] * prefix *Math.Exp(-0.5 *distance);
}
result += Math.Log(mixtureResult);
}
return(result);
}
/// <summary>
/// 1. Calculate Mahalanobis Distance for exponent factor
/// 2. Check if the matrix is semetric
/// 3. Check if the matrix is positive and semidifine
/// 4. Calculate Inverse matrix
/// 5. Check if matrix is Positive definite
/// </summary>
/// <param name="x">Observation vector</param>
/// <returns>Probability</returns>
public override double ProbabilityDensityFunction(params double[] x)
{
var k = x.Length;
var sigmaInverse = _matrix.Inverse();
var distance = Mahalanobis.Calculate(x, Mean, sigmaInverse);
var constant = (1 / Math.Pow(SqrtPi, k)) * (1 / Math.Sqrt(_matrix.Determinant));
var p = constant * Math.Exp(-0.5 * distance);
// This means that the probability is to low (underflow)
if (p.EqualsToZero() || double.IsNaN(p))
{
p = MINIMUM_PROBABILITY;
}
// if (p > 1 || p < 0)
// {
// Debug.Write(Environment.NewLine + "Covariance matrix " + Environment.NewLine);
// Debug.Write(_matrix.ToString());
// Debug.Write(Environment.NewLine + "Mean Vector " + Environment.NewLine);
// Debug.Write((new Vector(Mean)).ToString());
// Debug.Write(Environment.NewLine + "Observation Vector " + Environment.NewLine);
// Debug.Write((new Vector(x)).ToString());
// Debug.Write(Environment.NewLine);
// //throw new ApplicationException(string.Format("Probability function value {0} must be in range [0..1]", p));
// }
return(p > 1 ? 1 : p);
}
/// <summary>
/// Caclulates Loglikelihood of Multivariate Gaussian Distribution
/// </summary>
/// <param name="observations">Observarion Sequence</param>
/// <param name="covariance">Covariance Matrixe</param>
/// <param name="mean">Mean Vector</param>
/// <returns>Loglikelihood</returns>
public static double Calculate(double[][] observations, double[,] covariance, double[] mean)
{
var N = observations.Length;
var D = covariance.GetLength(0);
var constant = N * D * 0.5 * Math.Log(2 * Math.PI);
var covarianceMatrix = new Matrix(covariance);
var covarianceMatrixInverse = covarianceMatrix.Inverse();
var lnCovariance = N * 0.5 * Math.Log(covarianceMatrix.Determinant);
var sumObservations = 0.0;
for (int n = 0; n < N; n++)
{
var x = observations[n];
var distance = Mahalanobis.Calculate(x, mean, covarianceMatrixInverse);
sumObservations += distance;
}
return(-constant - lnCovariance - 0.5 * sumObservations);
}
public void Calculate_MeanVectorAndCovarianceMatrixAndVector_MahalanobisDistance()
{
var m = new double[] { 500, 500 };
var x = new double[] { 410, 400 };
var sigma = new double[2, 2];
sigma[0, 0] = 6291.55737;
sigma[0, 1] = 3754.32851;
sigma[1, 0] = 3754.32851;
sigma[1, 1] = 6280.77066;
var matrix = new Matrix(sigma);
var sigmaInverse = matrix.Inverse();
sigmaInverse[0, 0] = Math.Round(sigmaInverse[0, 0], 5);
sigmaInverse[0, 1] = Math.Round(sigmaInverse[0, 1], 5);
sigmaInverse[1, 0] = Math.Round(sigmaInverse[1, 0], 5);
sigmaInverse[1, 1] = Math.Round(sigmaInverse[1, 1], 5);
var d = Mahalanobis.Calculate(x, m, sigmaInverse);
Assert.AreEqual(1.825, Math.Round(d, 3));
}