/// <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);
}
public void doc_mahalanobis()
{
#region doc_mahalanobis_3
// Let's say we would like to compute the Mahalanobis
// distance between the two vectors x and y below:
double[] x = { 2, 5, 1 };
double[] y = { 4, 2, 2 };
// Using the covariance
double[,] covariance =
{
{ 4, 3, 0 },
{ 3, 5, 2 },
{ 0, 2, 6 }
};
// There are multiple ways to create a Mahalanobis
// distance. The easiest method by far is by using:
var mahalanobis = Mahalanobis.FromCovarianceMatrix(covariance);
// Then, you can compute the distance using:
double distance = mahalanobis.Distance(x, y);
// However, if you need more control over how the covariance matrix
// should be inverted, or if you have the precision matrix instead of
// the covariance, you can use any of the alternative methods:
var fromCholesky = new Mahalanobis(new CholeskyDecomposition(covariance));
var fromSVD = new Mahalanobis(new SingularValueDecomposition(covariance));
var fromPrecision1 = new Mahalanobis(covariance.Inverse());
var fromPrecision2 = Mahalanobis.FromPrecisionMatrix(covariance.Inverse());
// They all should produce equivalent results:
double a = fromCholesky.Distance(x, y);
double b = fromSVD.Distance(x, y);
double c = fromPrecision1.Distance(x, y);
double d = fromPrecision2.Distance(x, y);
#endregion
double expected = Distance.Mahalanobis(x, y, new CholeskyDecomposition(covariance));
Assert.AreEqual(3.5185224171518357, expected, 1e-10);
Assert.AreEqual(expected, distance, 1e-10);
Assert.AreEqual(distance, a, 1e-10);
Assert.AreEqual(distance, b, 1e-10);
Assert.AreEqual(distance, c, 1e-10);
Assert.AreEqual(distance, d, 1e-10);
}
public static double MahalanobisMetrics(int row, int rowToCount)
{
var columns = GetColumnsWithoutLast();
if (InverseCovarianceMatrix == null)
{
var matrix = new double[Dt.Rows.Count, columns.Count];
for (int rowC = 0; rowC < Dt.Rows.Count; rowC++)
{
for (int colC = 0; colC < columns.Count; colC++)
{
matrix[rowC, colC] = Convert.ToDouble(Dt.Rows[rowC][colC]);
}
}
var covarianceMatrix = matrix.Covariance();
try
{
InverseCovarianceMatrix = covarianceMatrix.Inverse();
}
catch
{
InverseCovarianceMatrix = covarianceMatrix.PseudoInverse();
}
}
double[] xValues = new double[columns.Count];
double[] yValues = new double[columns.Count];
for (int a = 0; a < columns.Count; a++)
{
double x = Convert.ToDouble(Dt.Rows[row][a]);
double y = Convert.ToDouble(Dt.Rows[rowToCount][a]);
xValues[a] = x;
yValues[a] = y;
}
return(Mahalanobis.FromPrecisionMatrix(InverseCovarianceMatrix).Distance(xValues, yValues));
}
/// <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));
}
private double[,] mahalanobisMethod()
{
var mainWindow = (MainWindow)Application.Current.MainWindow;
var format = new NumberFormatInfo();
format.NegativeSign = "-";
int i = 0;
double[,] distances = new double[mainWindow.gridData.Rows.Count, mainWindow.gridData.Rows.Count];
double[,] table = new double[mainWindow.gridData.Rows.Count, mainWindow.gridData.Columns.Count - 1];
//double[,] table = new double[5,3];
//table[0, 0] = 64;
//table[0, 1] = 580;
//table[0, 2] = 29;
//table[1, 0] = 66;
//table[1, 1] = 570;
//table[1, 2] = 33;
//table[2, 0] = 68;
//table[2, 1] = 590;
//table[2, 2] = 37;
//table[3, 0] = 69;
//table[3, 1] = 660;
//table[3, 2] = 46;
//table[4, 0] = 73;
//table[4, 1] = 600;
//table[4, 2] = 55;
foreach (DataRow row in mainWindow.gridData.Rows)
{
for (int j = 0; j < mainWindow.gridData.Columns.Count - 1; j++)
{
var value = mainWindow.gridData.Rows[i][j].ToString();
if (value.StartsWith(",") || value.StartsWith("."))
{
value = "0" + value;
}
table[i, j] = Convert.ToDouble(value, format);
}
i++;
}
double[] d = new double[mainWindow.gridData.Columns.Count - 1];
double[,] diff = new double[1, mainWindow.gridData.Columns.Count - 1];
double[,] diffT = null;
double[,] covarMatrix = table.Covariance();
double[,] inverseCovarMatrix = null;
double[,] tmp = null;
double[,] squaredDist = null;
try
{
inverseCovarMatrix = covarMatrix.Inverse();
}
catch (Exception exp)
{
inverseCovarMatrix = covarMatrix.PseudoInverse();
}
var mahalanobis = Mahalanobis.FromPrecisionMatrix(inverseCovarMatrix);
List <double> X = new List <double>();
List <double> Y = new List <double>();
for (int k = 0; k < mainWindow.gridData.Rows.Count; k++)
{
for (int n = 0; n < mainWindow.gridData.Rows.Count; n++)
{
if (k == n)
{
distances[k, n] = 0;
}
else
{
X.Clear();
Y.Clear();
for (int j = 0; j < mainWindow.gridData.Columns.Count - 1; j++)
{
var valueK = mainWindow.gridData.Rows[k][j].ToString();
if (valueK.StartsWith(",") || valueK.StartsWith("."))
{
valueK = "0" + valueK;
}
var valueN = mainWindow.gridData.Rows[n][j].ToString();
if (valueN.StartsWith(",") || valueN.StartsWith("."))
{
valueN = "0" + valueN;
}
//d[j] = Convert.ToDouble(valueK, format) - Convert.ToDouble(valueN, format);
// diff[0, j] = d[j];
X.Add(Convert.ToDouble(valueK, format));
Y.Add(Convert.ToDouble(valueN, format));
}
//diffT = Transpose(diff);
// covarMatrix = table.Covariance();
//try
//{
// inverseCovarMatrix = covarMatrix.Inverse();
//}
//catch(Exception exp)
//{
// inverseCovarMatrix = covarMatrix.PseudoInverse();
//}
//var mahalanobis = Mahalanobis.FromPrecisionMatrix(inverseCovarMatrix);
double result = mahalanobis.Distance(X.ToArray(), Y.ToArray());
//tmp = MultiplyMatrix(diff, inverseCovarMatrix);
//squaredDist = MultiplyMatrix(tmp, diffT);
//double result = Math.Sqrt(squaredDist[0, 0]);
if (Double.IsNaN(result))
{
distances[k, n] = 0;
}
else
{
distances[k, n] = result;
}
}
}
}
return(distances);
}
public KAverageWindow()
{
InitializeComponent();
mainWindow = (MainWindow)Application.Current.MainWindow;
metrics = new List <string>()
{
"metryka euklidesowa",
"metryka Manhattan",
"metryka Czebyszewa",
"metryka Mahalanobisa"
};
metricsComboBox.ItemsSource = metrics;
distinctClasses = (from row in mainWindow.gridData.AsEnumerable()
select row.Field <string>(mainWindow.gridData.Columns[mainWindow.gridData.Columns.Count - 1].ColumnName)).Distinct().ToList();
copiedTable = mainWindow.gridData.Copy();
copiedTable.Columns.RemoveAt(copiedTable.Columns.Count - 1);
for (int z = 0; z < copiedTable.Rows.Count; z++)
{
var newRow = tableWithNewColumns.NewRow();
tableWithNewColumns.Rows.Add(newRow);
}
//var mainWindow = (MainWindow)Application.Current.MainWindow;
var format = new NumberFormatInfo();
format.NegativeSign = "-";
int i = 0;
double[,] table = new double[mainWindow.gridData.Rows.Count, mainWindow.gridData.Columns.Count - 1];
foreach (DataRow row in mainWindow.gridData.Rows)
{
for (int j = 0; j < mainWindow.gridData.Columns.Count - 1; j++)
{
var value = mainWindow.gridData.Rows[i][j].ToString();
if (value.StartsWith(",") || value.StartsWith("."))
{
value = "0" + value;
}
table[i, j] = Convert.ToDouble(value, format);
}
i++;
}
double[] d = new double[mainWindow.gridData.Columns.Count - 1];
double[,] diff = new double[1, mainWindow.gridData.Columns.Count - 1];
double[,] covarMatrix = table.Covariance();
double[,] inverseCovarMatrix = null;
try
{
inverseCovarMatrix = covarMatrix.Inverse();
}
catch (Exception exp)
{
inverseCovarMatrix = covarMatrix.PseudoInverse();
}
mahalanobis = Mahalanobis.FromPrecisionMatrix(inverseCovarMatrix);
}