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MahalanobisDistance Method

Computes the distance d(x,y) between points x and y.

Namespace:  Accord.Math.Distances
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0
public double Distance(
	double[] x,
	double[] y
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Type: SystemDouble
The first point x.
Type: SystemDouble
The second point y.

Return Value

Type: Double
A double-precision value representing the distance d(x,y) between x and y according to the distance function implemented by this class.


IDistanceT, UDistance(T, U)
// 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);
See Also