This class implements AMF (alternating matrix factorization) on the given matrix V. More...

#include <amf.hpp>

Public Member Functions
	AMF (const TerminationPolicyType &terminationPolicy=TerminationPolicyType(), const InitializationRuleType &initializeRule=InitializationRuleType(), const UpdateRuleType &update=UpdateRuleType())
	Create the AMF object and (optionally) set the parameters which AMF will run with. More...

template<typename MatType >
double	Apply (const MatType &V, const size_t r, arma::mat &W, arma::mat &H)
	Apply Alternating Matrix Factorization to the provided matrix. More...

const TerminationPolicyType &	TerminationPolicy () const
	Access the termination policy.

TerminationPolicyType &	TerminationPolicy ()
	Modify the termination policy.

const InitializationRuleType &	InitializeRule () const
	Access the initialization rule.

InitializationRuleType &	InitializeRule ()
	Modify the initialization rule.

const UpdateRuleType &	Update () const
	Access the update rule.

UpdateRuleType &	Update ()
	Modify the update rule.

Detailed Description

template<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomAcolInitialization<>, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate>
class mlpack::amf::AMF< TerminationPolicyType, InitializationRuleType, UpdateRuleType >

This class implements AMF (alternating matrix factorization) on the given matrix V.

Alternating matrix factorization decomposes V in the form \( V \approx WH \) where W is called the basis matrix and H is called the encoding matrix. V is taken to be of size n x m and the obtained W is n x r and H is r x m. The size r is called the rank of the factorization.

The implementation requires three template types; the first contains the policy used to determine when the algorithm has converged; the second contains the initialization rule for the W and H matrix; the last contains the update rule to be used during each iteration. This templatization allows the user to try various update rules, initialization rules, and termination policies (including ones not supplied with mlpack) for factorization. By default, the template parameters to AMF implement non-negative matrix factorization with the multiplicative distance update.

A simple example of how to run AMF (or NMF) is shown below.

extern arma::mat V; // Matrix that we want to perform LMF on.
size_t r = 10; // Rank of decomposition
arma::mat W; // Basis matrix
arma::mat H; // Encoding matrix
AMF<> amf; // Default options: NMF with multiplicative distance update rules.
amf.Apply(V, r, W, H);

Template Parameters

TerminationPolicy	The policy to use for determining when the factorization has converged.
InitializationRule	The initialization rule for initializing W and H matrix.
UpdateRule	The update rule for calculating W and H matrix at each iteration.

See also: NMFMultiplicativeDistanceUpdate, SimpleResidueTermination

Constructor & Destructor Documentation

◆ AMF()

template<typename TerminationPolicyType , typename InitializationRuleType , typename UpdateRuleType >

mlpack::amf::AMF< TerminationPolicyType, InitializationRuleType, UpdateRuleType >::AMF	(	const TerminationPolicyType &	terminationPolicy = `TerminationPolicyType()`,
		const InitializationRuleType &	initializeRule = `InitializationRuleType()`,
		const UpdateRuleType &	update = `UpdateRuleType()`
	)

Create the AMF object and (optionally) set the parameters which AMF will run with.

Construct the AMF object.

The minimum residue refers to the root mean square of the difference between two subsequent iterations of the product W * H. A low residue indicates that subsequent iterations are not producing much change in W and H. Once the residue goes below the specified minimum residue, the algorithm terminates.

Parameters

initializeRule	Optional instantiated InitializationRule object for initializing the W and H matrices.
update	Optional instantiated UpdateRule object; this parameter is useful when the update rule for the W and H vector has state that it needs to store (i.e. HUpdate() and WUpdate() are not static functions).
terminationPolicy	Optional instantiated TerminationPolicy object.

Member Function Documentation

◆ Apply()

template<typename TerminationPolicyType , typename InitializationRuleType , typename UpdateRuleType >

template<typename MatType >

double mlpack::amf::AMF< TerminationPolicyType, InitializationRuleType, UpdateRuleType >::Apply	(	const MatType &	V,
		const size_t	r,
		arma::mat &	W,
		arma::mat &	H
	)

Apply Alternating Matrix Factorization to the provided matrix.