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mlpack
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The Mahalanobis distance, which is essentially a stretched Euclidean distance. More...
#include <mahalanobis_distance.hpp>
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 (arma::mat covariance) | |
| Initialize the Mahalanobis distance with the given covariance matrix. More... | |
| template<typename VecTypeA , typename VecTypeB > | |
| double | Evaluate (const VecTypeA &a, const VecTypeB &b) |
| Evaluate the distance between the two given points using this Mahalanobis distance. More... | |
| const arma::mat & | Covariance () const |
| Access the covariance matrix. More... | |
| arma::mat & | Covariance () |
| Modify the covariance matrix. More... | |
| template<typename Archive > | |
| void | serialize (Archive &ar, const uint32_t version) |
| Serialize the Mahalanobis distance. | |
| template<> | |
| double | Evaluate (const VecTypeA &a, const VecTypeB &b) |
| Specialization for non-rooted case. | |
| template<> | |
| double | Evaluate (const VecTypeA &a, const VecTypeB &b) |
| Specialization for rooted case. More... | |
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 is typically much quicker to use an LMetric and simply stretch the actual dataset itself before performing any evaluations. However, this class is provided for convenience.
If you wish to use the KNN class or other tree-based algorithms with this distance, it is recommended to instead stretch the dataset first, by decomposing Q = L^T L (perhaps via a Cholesky decomposition), and then multiply the data by L. If you still wish to use the KNN class with a custom distance anyway, you will need to use a different tree type than the default KDTree, which only works with the LMetric class.
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.
| TakeRoot | If 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. |
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Initialize the Mahalanobis distance with the empty matrix as covariance.
Don't call Evaluate() until you set the covariance with Covariance()!
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inline |
Initialize the Mahalanobis distance with the identity matrix of the given dimensionality.
| dimensionality | Dimesnsionality of the covariance matrix. |
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inline |
Initialize the Mahalanobis distance with the given covariance matrix.
The given covariance matrix will be copied (this is not optimal).
| covariance | The covariance matrix to use for this distance. |
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inline |
Access the covariance matrix.
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inline |
Modify the covariance matrix.
| double mlpack::metric::MahalanobisDistance< true >::Evaluate | ( | const VecTypeA & | a, |
| const VecTypeB & | b | ||
| ) |
Specialization for rooted case.
This requires one extra evaluation of sqrt().
| double mlpack::metric::MahalanobisDistance< TakeRoot >::Evaluate | ( | const VecTypeA & | a, |
| const VecTypeB & | b | ||
| ) |
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.
| a | First vector. |
| b | Second vector. |
1.8.13