MahalanobisDistance (imagingbook-common 1.4-SNAPSHOT API)

java.lang.Object
- imagingbook.lib.math.VectorNorm
- - imagingbook.lib.math.MahalanobisDistance

```
public class MahalanobisDistance
extends VectorNorm
```
This class implements the Mahalanobis distance using the Apache commons math library. See the numerical example in Theodoridis/Koutumbras, "Pattern recognition", p. 27.

Nested Class Summary
- Nested classes/interfaces inherited from class imagingbook.lib.math.VectorNorm
  VectorNorm.L1, VectorNorm.L2, VectorNorm.Linf, VectorNorm.NormType

Field Summary

Fields
Modifier and Type Field and Description

static boolean BIAS_CORRECTION

static double DEFAULT_DIAGONAL_INCREMENT

Fields
Modifier and Type	Field and Description
`static boolean`	`BIAS_CORRECTION`
`static double`	`DEFAULT_DIAGONAL_INCREMENT`

Constructor Summary

Constructors
Constructor and Description
`MahalanobisDistance(double[][] samples)` Create a new instance from an array of m-dimensional samples, e.g.
`MahalanobisDistance(double[][] samples, double diagonalIncrement)` Create a new instance from an array of m-dimensional samples, e.g.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`distance(double[] X)` Calculates the Mahalanobis distance between point X and the mean of the reference distribution.
`double`	`distance(double[] X, double[] Y)` Calculates the distance between two vectors.
`double`	`distance(float[] a, float[] b)`
`double`	`distance(int[] a, int[] b)`
`double`	`distance2(double[] X)` Calculates the sqared Mahalanobis distance between point X and the mean of the reference distribution.
`double`	`distance2(double[] X, double[] Y)`
`double`	`distance2(float[] a, float[] b)`
`double`	`distance2(int[] a, int[] b)`
`double[][]`	`getCovarianceMatrix()`
`double[][]`	`getInverseCovarianceMatrix()`
`double[]`	`getMeanVector()`
`int`	`getNumberOfSamples()`
`int`	`getSampleDimension()`
`double`	`getScale(int n)` Returns a factor to scale magnitude and distance values to the range of the vector components of dimensionality n.
`double[][]`	`getWhiteningTransformation()` Returns the 'root' (U) of the inverse covariance matrix S^{-1}, such that S^{-1} = U^T .
`double`	`magnitude(double[] X)`
`double`	`magnitude(int[] X)`
`static void`	`main(String[] args)` Test example from Burger/Burge UTICS-C Appendix: N = 4 samples, K = 3 dimensions

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - DEFAULT_DIAGONAL_INCREMENT
```
public static final double DEFAULT_DIAGONAL_INCREMENT
```
    See Also:
    
    Constant Field Values
  - BIAS_CORRECTION
```
public static final boolean BIAS_CORRECTION
```
    See Also:
    
    Constant Field Values
- Constructor Detail
  - MahalanobisDistance
```
public MahalanobisDistance(double[][] samples,
                           double diagonalIncrement)
```
    Create a new instance from an array of m-dimensional samples, e.g. samples = {{x1,y1}, {x2,y2},...,{xn,yn}} for a vector of n two-dimensional samples.
    
    Parameters:
    
    samples - A vector of length n with m-dimensional samples, i.e. samples[k][i] represents the i-th component of the k-th sample.
    
    diagonalIncrement - Quantity added to the diagonal values of the covariance matrix to avoid singularity.
  - MahalanobisDistance
```
public MahalanobisDistance(double[][] samples)
```
    Create a new instance from an array of m-dimensional samples, e.g. samples = {{x1,y1}, {x2,y2},...,{xn,yn}} for a vector of n two-dimensional samples.
    
    Parameters:
    
    samples - A vector of length n with m-dimensional samples, i.e. samples[k][i] represents the i-th component of the k-th sample.
- Method Detail
  - getNumberOfSamples
```
public int getNumberOfSamples()
```
  - getSampleDimension
```
public int getSampleDimension()
```
  - getCovarianceMatrix
```
public double[][] getCovarianceMatrix()
```
  - getInverseCovarianceMatrix
```
public double[][] getInverseCovarianceMatrix()
```
  - getMeanVector
```
public double[] getMeanVector()
```
  - getWhiteningTransformation
```
public double[][] getWhiteningTransformation()
```
    Returns the 'root' (U) of the inverse covariance matrix S^{-1}, such that S^{-1} = U^T . U This matrix can be used to pre-transform the original sample vectors X (by X → U . X) to a space where distance measurement (in the Mahalanobis sense) can be calculated with the usual Euclidean norm. The matrix U is invertible in case the reverse mapping is required.
    
    Returns:
    
    The matrix for pre-transforming the original sample vectors.
  - distance
```
public double distance(double[] X,
                       double[] Y)
```
    Description copied from class: VectorNorm
    
    Calculates the distance between two vectors.
    
    Specified by:
    
    distance in class VectorNorm
    
    Parameters:
    
    X - first vector
    
    Y - second vector
    
    Returns:
    
    the distance between vectors a and b
  - distance2
```
public double distance2(double[] X,
                        double[] Y)
```
    Specified by:
    
    distance2 in class VectorNorm
    
    Parameters:
    
    X - first vector
    
    Y - second vector
    
    Returns:
    
    the squared distance between vectors a and b
  - distance
```
public double distance(double[] X)
```
    Calculates the Mahalanobis distance between point X and the mean of the reference distribution.
    
    Parameters:
    
    X - an arbitrary K-dimensional vector
    
    Returns:
    
    Mahalanobis distance between the point X and the mean of the reference distribution.
  - distance2
```
public double distance2(double[] X)
```
    Calculates the sqared Mahalanobis distance between point X and the mean of the reference distribution.
    
    Parameters:
    
    X - an arbitrary K-dimensional vector
    
    Returns:
    
    squared Mahalanobis distance between the point X and the mean of the reference distribution.
  - distance
```
public double distance(int[] a,
                       int[] b)
```
    Specified by:
    
    distance in class VectorNorm
  - distance2
```
public double distance2(int[] a,
                        int[] b)
```
    Specified by:
    
    distance2 in class VectorNorm
  - magnitude
```
public double magnitude(double[] X)
```
    Specified by:
    
    magnitude in class VectorNorm
  - magnitude
```
public double magnitude(int[] X)
```
    Specified by:
    
    magnitude in class VectorNorm
  - getScale
```
public double getScale(int n)
```
    Description copied from class: VectorNorm
    
    Returns a factor to scale magnitude and distance values to the range of the vector components of dimensionality n. This is prim. used for scaling color distances (n = 3). E.g., if components are distributed in [0,255], the distances multiplied by this factor should again be in [0,255].
    
    Specified by:
    
    getScale in class VectorNorm
    
    Parameters:
    
    n - dimensionality
    
    Returns:
    
    scale factor
  - distance
```
public double distance(float[] a,
                       float[] b)
```
    Specified by:
    
    distance in class VectorNorm
  - distance2
```
public double distance2(float[] a,
                        float[] b)
```
    Specified by:
    
    distance2 in class VectorNorm
  - main
```
public static void main(String[] args)
```
    Test example from Burger/Burge UTICS-C Appendix: N = 4 samples, K = 3 dimensions
    
    Parameters:
    
    args - ignored

Class MahalanobisDistance

Nested Class Summary

Nested classes/interfaces inherited from class imagingbook.lib.math.VectorNorm

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_DIAGONAL_INCREMENT

BIAS_CORRECTION

Constructor Detail

MahalanobisDistance

MahalanobisDistance

Method Detail

getNumberOfSamples

getSampleDimension

getCovarianceMatrix

getInverseCovarianceMatrix

getMeanVector

getWhiteningTransformation

distance

distance2

distance

distance2

distance

distance2

magnitude

magnitude

getScale

distance

distance2

main