mlpack::metric::LMetric< TPower, TTakeRoot > Class Template Reference

The L_p metric for arbitrary integer p, with an option to take the root. More...

#include <lmetric.hpp>

Public Member Functions
	LMetric ()
	Default constructor does nothing, but is required to satisfy the Metric policy.
template<typename Archive >
void	serialize (Archive &, const uint32_t)
	Serialize the metric (nothing to do).
template<>
VecTypeA::elem_type	Evaluate (const VecTypeA &a, const VecTypeB &b)
template<>
VecTypeA::elem_type	Evaluate (const VecTypeA &a, const VecTypeB &b)
template<>
VecTypeA::elem_type	Evaluate (const VecTypeA &a, const VecTypeB &b)
template<>
VecTypeA::elem_type	Evaluate (const VecTypeA &a, const VecTypeB &b)
template<>
VecTypeA::elem_type	Evaluate (const VecTypeA &a, const VecTypeB &b)
template<>
VecTypeA::elem_type	Evaluate (const VecTypeA &a, const VecTypeB &b)
template<>
VecTypeA::elem_type	Evaluate (const VecTypeA &a, const VecTypeB &b)

Static Public Member Functions
template<typename VecTypeA , typename VecTypeB >
static VecTypeA::elem_type	Evaluate (const VecTypeA &a, const VecTypeB &b)
	Computes the distance between two points. More...

Static Public Attributes
static const int	Power = TPower
	The power of the metric.
static const bool	TakeRoot = TTakeRoot
	Whether or not the root is taken.

Detailed Description

template<int TPower, bool TTakeRoot = true>
class mlpack::metric::LMetric< TPower, TTakeRoot >

The L_p metric for arbitrary integer p, with an option to take the root.

This class implements the standard L_p metric for two arbitrary vectors \( x \) and \( y \) of dimensionality \( n \):

\[ d(x, y) = \left( \sum_{i = 1}^{n} | x_i - y_i |^p \right)^{\frac{1}{p}}. \]

The value of p is given as a template parameter.

In addition, the function \( d(x, y) \) can be simplified, neglecting the p-root calculation. This is done by specifying the TakeRoot template parameter to be false. Then,

\[ d(x, y) = \sum_{i = 1}^{n} | x_i - y_i |^p \]

It is faster to compute that distance, so TakeRoot is by default off. However, when TakeRoot is false, the distance given is not actually a true metric – it does not satisfy the triangle inequality. Some mlpack methods do not require the triangle inequality to operate correctly (such as the BinarySpaceTree), but setting TakeRoot = false in some cases will cause incorrect results.

A few convenience typedefs are given:

• ManhattanDistance
• EuclideanDistance
• SquaredEuclideanDistance

Template Parameters

Power	Power of metric; i.e. Power = 1 gives the L1-norm (Manhattan distance).
TakeRoot	If true, the Power'th root of the result is taken before it is returned. Setting this to false causes the metric to not satisfy the Triangle Inequality (be careful!).

Member Function Documentation

Evaluate()

template<int Power, bool TakeRoot>

template<typename VecTypeA , typename VecTypeB >

VecTypeA::elem_type mlpack::metric::LMetric< Power, TakeRoot >::Evaluate ( const VecTypeA &  a, const VecTypeB &  b  )

static

Computes the distance between two points.

Template Parameters

VecTypeA	Type of first vector (generally arma::vec or arma::sp_vec).
VecTypeB	Type of second vector.

Parameters

a	First vector.
b	Second vector.

Returns

Distance between vectors a and b.

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

• src/mlpack/core/metrics/lmetric.hpp
• src/mlpack/core/metrics/lmetric_impl.hpp