Catalano.Math.Distances

Class Distance

java.lang.Object

Catalano.Math.Distances.Distance

public final class Distance
extends java.lang.Object

Defines a set of extension methods defining distance measures. References: http://www.ajmaa.org/RGMIA/papers/v7n4/Gsdmi_RGMIA.pdf http://arabic-icr.googlecode.com/git/Papers/Comprehensive%20Survey%20on%20Distance-Similarity.pdf

Method Summary

Modifier and Type	Method and Description
static double	ArithmeticGeometricDivergence(double[] p, double[] q)
static double	Bhattacharyya(double[] histogram1, double[] histogram2) Bhattacharyya distance between two normalized histograms.
static double	BrayCurtis(double[] p, double[] q) Gets the Bray Curtis distance between two points.
static double	BrayCurtis(double x1, double y1, double x2, double y2) Gets the Bray Curtis distance between two points.
static double	BrayCurtis(IntPoint p, IntPoint q) Gets the Bray Curtis distance between two points.
static double	Canberra(double[] p, double[] q) Gets the Canberra distance between two points.
static double	Canberra(double x1, double y1, double x2, double y2) Gets the Canberra distance between two points.
static double	Canberra(IntPoint p, IntPoint q) Gets the Canberra distance between two points.
static double	Chebyshev(double[] p, double[] q) Gets the Chebyshev distance between two points.
static double	Chebyshev(double x1, double y1, double x2, double y2) Gets the Chebyshev distance between two points.
static double	Chebyshev(IntPoint p, IntPoint q) Gets the Chebyshev distance between two points.
static double	Chessboard(double[] x, double[] y) Gets the Chessboard distance between two points.
static double	Chessboard(double x1, double y1, double x2, double y2) Gets the Chessboard distance between two points.
static double	Chessboard(IntPoint p, IntPoint q) Gets the Chessboard distance between two points.
static double	ChiSquare(double[] histogram1, double[] histogram2) Gets the Chi Square distance between two normalized histograms.
static double	Correlation(double[] p, double[] q) Gets the Correlation distance between two points.
static double	Cosine(double[] p, double[] q) Gets the Cosine distance between two points.
static double	Cosine(double x1, double y1, double x2, double y2) Gets the Cosine distance between two points.
static double	Cosine(IntPoint p, IntPoint q) Gets the Cosine distance between two points.
static double	Euclidean(double[] p, double[] q) Gets the Euclidean distance between two points.
static double	Euclidean(double x1, double y1, double x2, double y2) Gets the Euclidean distance between two points.
static double	Euclidean(IntPoint p, IntPoint q) Gets the Euclidean distance between two points.
static int	Hamming(java.lang.String first, java.lang.String second) Gets the Hamming distance between two strings.
static double	JaccardDistance(double[] p, double[] q) Gets the Jaccard distance between two points.
static double	JDivergence(double[] p, double[] q) Gets the J-Divergence.
static double	JensenDifferenceDivergence(double[] p, double[] q) Gets the Jensen difference divergence.
static double	JensenShannonDivergence(double[] p, double[] q) Gets the Jensen Shannon divergence.
static double	KDivergence(double[] p, double[] q) Gets the K-Divergence.
static double	KullbackLeiblerDivergence(double[] p, double[] q) Gets the Kullback Leibler divergence.
static double	KumarJohnsonDivergence(double[] p, double[] q) Gets the Kumar-Johnson divergence.
static double	Mahalanobis(double[][] A, double[][] B) Gets the Mahalanobis distance.
static double	Manhattan(double[] p, double[] q) Gets the Manhattan distance between two points.
static double	Manhattan(double x1, double y1, double x2, double y2) Gets the Manhattan distance between two points.
static double	Manhattan(IntPoint p, IntPoint q) Gets the Manhattan distance between two points.
static double	Minkowski(double[] u, double[] v, double p) Gets the Minkowski distance between two points.
static double	Minkowski(double x1, double y1, double x2, double y2, int r) Gets the Minkowski distance between two points.
static double	Minkowski(IntPoint p, IntPoint q, int r) Gets the Minkowski distance between two points.
static double	QuasiEuclidean(double x1, double y1, double x2, double y2) Gets the Quasi-Euclidean distance between two points.
static double	QuasiEuclidean(IntPoint p, IntPoint q) Gets the Quasi-Euclidean distance between two points.
static double	SquaredEuclidean(double[] x, double[] y) Gets the Square Euclidean distance between two points.
static double	SquaredEuclidean(double x1, double y1, double x2, double y2) Gets the Squared Euclidean distance between two points.
static double	SquaredEuclidean(IntPoint p, IntPoint q) Gets the Squared Euclidean distance between two points.
static double	SymmetricChiSquareDivergence(double[] p, double[] q) Gets the Symmetric Chi-square divergence.
static double	SymmetricKullbackLeibler(double[] p, double[] q) Gets the Symmetric Kullback-Leibler distance.
static double	Taneja(double[] p, double[] q) Gets the Taneja divergence.
static double	TopsoeDivergence(double[] p, double[] q) Gets the Topsoe divergence.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

ArithmeticGeometricDivergence

public static double ArithmeticGeometricDivergence(double[] p,
                                                   double[] q)

Bhattacharyya

public static double Bhattacharyya(double[] histogram1,
                                   double[] histogram2)

Bhattacharyya distance between two normalized histograms.

Parameters:

histogram1 - Normalized histogram.

histogram2 - Normalized histogram.

Returns:

The Bhattacharyya distance between the two histograms.

BrayCurtis

public static double BrayCurtis(double[] p,
                                double[] q)

Gets the Bray Curtis distance between two points.

Parameters:

p - A point in space.

q - A point in space.

Returns:

The Bray Curtis distance between x and y.

BrayCurtis

public static double BrayCurtis(double x1,
                                double y1,
                                double x2,
                                double y2)

Gets the Bray Curtis distance between two points.

Parameters:

x1 - X1 axis coordinate.

y1 - Y1 axis coordinate.

x2 - X2 axis coordinate.

y2 - X2 axis coordinate.

Returns:

The Bray Curtis distance between x and y.

BrayCurtis

public static double BrayCurtis(IntPoint p,
                                IntPoint q)

Gets the Bray Curtis distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

Returns:

The Bray Curtis distance between x and y.

Canberra

public static double Canberra(double[] p,
                              double[] q)

Gets the Canberra distance between two points.

Parameters:

p - A point in space.

q - A point in space.

Returns:

The Canberra distance between x and y.

Canberra

public static double Canberra(double x1,
                              double y1,
                              double x2,
                              double y2)

Gets the Canberra distance between two points.

Parameters:

x1 - X1 axis coordinate.

y1 - Y1 axis coordinate.

x2 - X2 axis coordinate.

y2 - Y2 axis coordinate.

Returns:

The Canberra distance between x and y.

Canberra

public static double Canberra(IntPoint p,
                              IntPoint q)

Gets the Canberra distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

Returns:

The Canberra distance between x and y.

Chebyshev

public static double Chebyshev(double[] p,
                               double[] q)

Gets the Chebyshev distance between two points.

Parameters:

p - A point in space.

q - A point in space.

Returns:

The Chebyshev distance between x and y.

Chebyshev

public static double Chebyshev(double x1,
                               double y1,
                               double x2,
                               double y2)

Gets the Chebyshev distance between two points.

Parameters:

x1 - X1 axis coordinate.

y1 - Y1 axis coordinate.

x2 - X2 axis coordinate.

y2 - Y2 axis coordinate.

Returns:

The Chebyshev distance between x and y.

Chebyshev

public static double Chebyshev(IntPoint p,
                               IntPoint q)

Gets the Chebyshev distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

Returns:

The Chebyshev distance between x and y.

Chessboard

public static double Chessboard(double[] x,
                                double[] y)

Gets the Chessboard distance between two points.

Parameters:

x - A point in space.

y - A point in space.

Returns:

The Chessboard distance between x and y.

Chessboard

public static double Chessboard(double x1,
                                double y1,
                                double x2,
                                double y2)

Gets the Chessboard distance between two points.

Parameters:

x1 - X1 axis coordinate.

y1 - Y1 axis coordinate.

x2 - X2 axis coordinate.

y2 - Y2 axis coordinate.

Returns:

The Chessboard distance between x and y.

Chessboard

public static double Chessboard(IntPoint p,
                                IntPoint q)

Gets the Chessboard distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

Returns:

The Chessboard distance between x and y.

ChiSquare

public static double ChiSquare(double[] histogram1,
                               double[] histogram2)

Gets the Chi Square distance between two normalized histograms.

Parameters:

histogram1 - Histogram.

histogram2 - Histogram.

Returns:

The Chi Square distance between x and y.

Correlation

public static double Correlation(double[] p,
                                 double[] q)

Gets the Correlation distance between two points.

Parameters:

p - A point in space.

q - A point in space.

Returns:

The Correlation distance between x and y.

Cosine

public static double Cosine(double[] p,
                            double[] q)

Gets the Cosine distance between two points.

Parameters:

p - A point in space.

q - A point in space.

Returns:

The Cosine distance between x and y.

Cosine

public static double Cosine(double x1,
                            double y1,
                            double x2,
                            double y2)

Gets the Cosine distance between two points.

Parameters:

x1 - X1 axis coordinate.

y1 - Y1 axis coordinate.

x2 - X2 axis coordinate.

y2 - Y2 axis coordinate.

Returns:

The Cosine distance between x and y.

Cosine

public static double Cosine(IntPoint p,
                            IntPoint q)

Gets the Cosine distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

Returns:

The Cosine distance between x and y.

Euclidean

public static double Euclidean(double[] p,
                               double[] q)

Gets the Euclidean distance between two points.

Parameters:

p - A point in space.

q - A point in space.

Returns:

The Euclidean distance between x and y.

Euclidean

public static double Euclidean(double x1,
                               double y1,
                               double x2,
                               double y2)

Gets the Euclidean distance between two points.

Parameters:

x1 - X1 axis coordinate.

y1 - Y1 axis coordinate.

x2 - X2 axis coordinate.

y2 - Y2 axis coordinate.

Returns:

The Euclidean distance between x and y.

Euclidean

public static double Euclidean(IntPoint p,
                               IntPoint q)

Gets the Euclidean distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

Returns:

The Euclidean distance between x and y.

Hamming

public static int Hamming(java.lang.String first,
                          java.lang.String second)

Gets the Hamming distance between two strings.

Parameters:

first - First string.

second - Second string.

Returns:

The Hamming distance between p and q.

JaccardDistance

public static double JaccardDistance(double[] p,
                                     double[] q)

Gets the Jaccard distance between two points.

Parameters:

p - A point in space.

q - A point in space.

Returns:

The Jaccard distance between x and y.

JDivergence

public static double JDivergence(double[] p,
                                 double[] q)

Gets the J-Divergence.

Parameters:

p - P vector.

q - Q vector.

Returns:

The J-Divergence between p and q.

JensenDifferenceDivergence

public static double JensenDifferenceDivergence(double[] p,
                                                double[] q)

Gets the Jensen difference divergence.

Parameters:

p - P vector.

q - Q vector.

Returns:

The Jensen difference between p and q.

JensenShannonDivergence

public static double JensenShannonDivergence(double[] p,
                                             double[] q)

Gets the Jensen Shannon divergence.

Parameters:

p - U vector.

q - V vector.

Returns:

The Jensen Shannon divergence between u and v.

KDivergence

public static double KDivergence(double[] p,
                                 double[] q)

Gets the K-Divergence.

Parameters:

p - U vector.

q - V vector.

Returns:

The K-Divergence between u and v.

KumarJohnsonDivergence

public static double KumarJohnsonDivergence(double[] p,
                                            double[] q)

Gets the Kumar-Johnson divergence.

Parameters:

p - P vector.

q - Q vector.

Returns:

The Kumar-Johnson divergence between p and q.

KullbackLeiblerDivergence

public static double KullbackLeiblerDivergence(double[] p,
                                               double[] q)

Gets the Kullback Leibler divergence.

Parameters:

p - P vector.

q - Q vector.

Returns:

The Kullback Leibler divergence between u and v.

Mahalanobis

public static double Mahalanobis(double[][] A,
                                 double[][] B)

Gets the Mahalanobis distance.

Parameters:

A - Matrix A.

B - Matrix B.

Returns:

The Mahalanobis distance between A and B.

Manhattan

public static double Manhattan(double[] p,
                               double[] q)

Gets the Manhattan distance between two points.

Parameters:

p - A point in space.

q - A point in space.

Returns:

The Manhattan distance between x and y.

Manhattan

public static double Manhattan(double x1,
                               double y1,
                               double x2,
                               double y2)

Gets the Manhattan distance between two points.

Parameters:

x1 - X1 axis coordinate.

y1 - Y1 axis coordinate.

x2 - X2 axis coordinate.

y2 - Y2 axis coordinate.

Returns:

The Manhattan distance between x and y.

Manhattan

public static double Manhattan(IntPoint p,
                               IntPoint q)

Gets the Manhattan distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

Returns:

The Manhattan distance between x and y.

Minkowski

public static double Minkowski(double x1,
                               double y1,
                               double x2,
                               double y2,
                               int r)

Gets the Minkowski distance between two points.

Parameters:

x1 - X1 axis coordinate.

y1 - Y1 axis coordinate.

x2 - X2 axis coordinate.

y2 - Y2 axis coordinate.

r - Order between two points.

Returns:

The Minkowski distance between x and y.

Minkowski

public static double Minkowski(IntPoint p,
                               IntPoint q,
                               int r)

Gets the Minkowski distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

r - Order between two points.

Returns:

The Minkowski distance between x and y.

Minkowski

public static double Minkowski(double[] u,
                               double[] v,
                               double p)

Gets the Minkowski distance between two points.

Parameters:

u - A point in space.

v - A point in space.

p - Order between two points.

Returns:

The Minkowski distance between x and y.

QuasiEuclidean

public static double QuasiEuclidean(double x1,
                                    double y1,
                                    double x2,
                                    double y2)

Gets the Quasi-Euclidean distance between two points.

Parameters:

x1 - X1 axis coordinates.

y1 - Y1 axis coordinates.

x2 - X2 axis coordinates.

y2 - Y2 axis coordinates.

Returns:

The Quasi-Euclidean distance between x and y.

QuasiEuclidean

public static double QuasiEuclidean(IntPoint p,
                                    IntPoint q)

Gets the Quasi-Euclidean distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

Returns:

The Quasi Euclidean distance between p and q.

SquaredEuclidean

public static double SquaredEuclidean(double[] x,
                                      double[] y)

Gets the Square Euclidean distance between two points.

Parameters:

x - A point in space.

y - A point in space.

Returns:

The Square Euclidean distance between x and y.

SquaredEuclidean

public static double SquaredEuclidean(double x1,
                                      double y1,
                                      double x2,
                                      double y2)

Gets the Squared Euclidean distance between two points.

Parameters:

x1 - X1 axis coordinates.

y1 - Y1 axis coordinates.

x2 - X2 axis coordinates.

y2 - Y2 axis coordinates.

Returns:

The Squared euclidean distance between x and y.

SquaredEuclidean

public static double SquaredEuclidean(IntPoint p,
                                      IntPoint q)

Gets the Squared Euclidean distance between two points.

Parameters:

p - IntPoint with X and Y axis coordinates.

q - IntPoint with X and Y axis coordinates.

Returns:

The Squared euclidean distance between x and y.

SymmetricChiSquareDivergence

public static double SymmetricChiSquareDivergence(double[] p,
                                                  double[] q)

Gets the Symmetric Chi-square divergence.

Parameters:

p - P vector.

q - Q vector.

Returns:

The Symmetric chi-square divergence between p and q.

SymmetricKullbackLeibler

public static double SymmetricKullbackLeibler(double[] p,
                                              double[] q)

Gets the Symmetric Kullback-Leibler distance. This metric is valid only for real and positive P and Q.

Parameters:

p - P vector.

q - Q vector.

Returns:

The Symmetric Kullback Leibler distance between p and q.

Taneja

public static double Taneja(double[] p,
                            double[] q)

Gets the Taneja divergence.

Parameters:

p - P vector.

q - Q vector.

Returns:

The Taneja divergence between p and q.

TopsoeDivergence

public static double TopsoeDivergence(double[] p,
                                      double[] q)

Gets the Topsoe divergence.

Parameters:

p - P vector.

q - Q vector.

Returns:

The Topsoe divergence between p and q.