MLPACK  1.0.11
Public Member Functions | Private Attributes | List of all members
mlpack::metric::MahalanobisDistance< TakeRoot > Class Template Reference

The Mahalanobis distance, which is essentially a stretched Euclidean distance. More...

Public Member Functions

 MahalanobisDistance ()
 Initialize the Mahalanobis distance with the empty matrix as covariance. More...
 
 MahalanobisDistance (const size_t dimensionality)
 Initialize the Mahalanobis distance with the identity matrix of the given dimensionality. More...
 
 MahalanobisDistance (const arma::mat &covariance)
 Initialize the Mahalanobis distance with the given covariance matrix. More...
 
const arma::mat & Covariance () const
 Access the covariance matrix. More...
 
arma::mat & Covariance ()
 Modify the covariance matrix. More...
 
template<typename VecType1 , typename VecType2 >
double Evaluate (const VecType1 &a, const VecType2 &b)
 
std::string ToString () const
 Evaluate the distance between the two given points using this Mahalanobis distance. More...
 

Private Attributes

arma::mat covariance
 The covariance matrix associated with this distance. More...
 

Detailed Description

template<bool TakeRoot = true>
class mlpack::metric::MahalanobisDistance< TakeRoot >

The Mahalanobis distance, which is essentially a stretched Euclidean distance.

Given a square covariance matrix $ Q $ of size $ d $ x $ d $, where $ d $ is the dimensionality of the points it will be evaluating, and given two vectors $ x $ and $ y $ also of dimensionality $ d $,

\[ d(x, y) = \sqrt{(x - y)^T Q (x - y)} \]

where Q is the covariance matrix.

Because each evaluation multiplies (x_1 - x_2) by the covariance matrix, it may be much quicker to use an LMetric and simply stretch the actual dataset itself before performing any evaluations. However, this class is provided for convenience.

Similar to the LMetric class, this offers a template parameter TakeRoot which, when set to false, will instead evaluate the distance

\[ d(x, y) = (x - y)^T Q (x - y) \]

which is faster to evaluate.

Template Parameters
TakeRootIf true, takes the root of the output. It is slightly faster to leave this at the default of false, but this means the metric may not satisfy the triangle inequality and may not be usable for methods that expect a true metric.

Definition at line 63 of file mahalanobis_distance.hpp.

Constructor & Destructor Documentation

template<bool TakeRoot = true>
mlpack::metric::MahalanobisDistance< TakeRoot >::MahalanobisDistance ( )
inline

Initialize the Mahalanobis distance with the empty matrix as covariance.

Don't call Evaluate() until you set the covariance with Covariance()!

Definition at line 70 of file mahalanobis_distance.hpp.

template<bool TakeRoot = true>
mlpack::metric::MahalanobisDistance< TakeRoot >::MahalanobisDistance ( const size_t  dimensionality)
inline

Initialize the Mahalanobis distance with the identity matrix of the given dimensionality.

Parameters
dimensionalityDimesnsionality of the covariance matrix.

Definition at line 78 of file mahalanobis_distance.hpp.

template<bool TakeRoot = true>
mlpack::metric::MahalanobisDistance< TakeRoot >::MahalanobisDistance ( const arma::mat &  covariance)
inline

Initialize the Mahalanobis distance with the given covariance matrix.

The given covariance matrix will be copied (this is not optimal).

Parameters
covarianceThe covariance matrix to use for this distance.

Definition at line 87 of file mahalanobis_distance.hpp.

References mlpack::metric::MahalanobisDistance< TakeRoot >::Evaluate(), and mlpack::metric::MahalanobisDistance< TakeRoot >::ToString().

Member Function Documentation

template<bool TakeRoot = true>
const arma::mat& mlpack::metric::MahalanobisDistance< TakeRoot >::Covariance ( ) const
inline

Access the covariance matrix.

Returns
Constant reference to the covariance matrix.

Definition at line 109 of file mahalanobis_distance.hpp.

References mlpack::metric::MahalanobisDistance< TakeRoot >::covariance.

template<bool TakeRoot = true>
arma::mat& mlpack::metric::MahalanobisDistance< TakeRoot >::Covariance ( )
inline

Modify the covariance matrix.

Returns
Reference to the covariance matrix.

Definition at line 116 of file mahalanobis_distance.hpp.

References mlpack::metric::MahalanobisDistance< TakeRoot >::covariance.

template<bool TakeRoot = true>
template<typename VecType1 , typename VecType2 >
double mlpack::metric::MahalanobisDistance< TakeRoot >::Evaluate ( const VecType1 &  a,
const VecType2 &  b 
)
template<bool TakeRoot = true>
std::string mlpack::metric::MahalanobisDistance< TakeRoot >::ToString ( ) const

Evaluate the distance between the two given points using this Mahalanobis distance.

If the covariance matrix has not been set (i.e. if you used the empty constructor and did not later modify the covariance matrix), calling this method will probably result in a crash.

Parameters
aFirst vector.
bSecond vector.

Referenced by mlpack::metric::MahalanobisDistance< TakeRoot >::MahalanobisDistance().

Member Data Documentation

template<bool TakeRoot = true>
arma::mat mlpack::metric::MahalanobisDistance< TakeRoot >::covariance
private

The covariance matrix associated with this distance.

Definition at line 119 of file mahalanobis_distance.hpp.

Referenced by mlpack::metric::MahalanobisDistance< TakeRoot >::Covariance().


The documentation for this class was generated from the following file: