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));
}
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);
}