SquareMahalanobis Structure

Squared Mahalanobis distance.

Namespace: Accord.Math.Distances
Assembly: Accord.Math (in Accord.Math.dll) Version: 3.8.0

Syntax

[SerializableAttribute]
public struct SquareMahalanobis : IMetric<double[]>, 
	IDistance<double[]>, IDistance<double[], double[]>

<SerializableAttribute>
Public Structure SquareMahalanobis
	Implements IMetric(Of Double()), IDistance(Of Double()), 
	IDistance(Of Double(), Double())

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The SquareMahalanobis type exposes the following members.

Constructors

	Name	Description
	SquareMahalanobis(Double)	Initializes a new instance of the Mahalanobis class.
	SquareMahalanobis(CholeskyDecomposition)	Initializes a new instance of the Mahalanobis class.
	SquareMahalanobis(SingularValueDecomposition)	Initializes a new instance of the Mahalanobis class.

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Methods

	Name	Description
	Distance	Computes the distance d(x,y) between points x and y.
	Equals	Indicates whether this instance and a specified object are equal. (Inherited from ValueType.)
	FromCovarianceMatrix	Creates a new Square-Mahalanobis distance from a covariance matrix.
	FromPrecisionMatrix	Creates a new Square-Mahalanobis distance from a precision matrix.
	GetHashCode	Returns the hash code for this instance. (Inherited from ValueType.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	ToString	Returns the fully qualified type name of this instance. (Inherited from ValueType.)

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Extension Methods

	Name	Description
	HasMethod	Checks whether an object implements a method with the given name. (Defined by ExtensionMethods.)
	IsEqual	Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices. (Defined by Matrix.)
	To(Type)	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)
	ToT	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)

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Examples

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// Let's say we would like to compute the Squared 
// Mahalanobis distance between the vectors 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 = SquareMahalanobis.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 SquareMahalanobis(new CholeskyDecomposition(covariance));
var fromSVD = new SquareMahalanobis(new SingularValueDecomposition(covariance));
var fromPrecision1 = new SquareMahalanobis(covariance.Inverse());
var fromPrecision2 = SquareMahalanobis.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);

Reference

Accord.Math.Distances Namespace