This class implements a method titled 'Alternating Least Squares' described in the following paper: More...

Public Member Functions
	NMFALSUpdate ()
	Empty constructor required for the UpdateRule template. More...

template<typename MatType >
void	Initialize (const MatType &, const size_t)
	Set initial values for the factorization. More...

template<typename Archive >
void	Serialize (Archive &, const unsigned int)
	Serialize the object (in this case, there is nothing to serialize). More...

Static Public Member Functions
template<typename MatType >
static void	HUpdate (const MatType &V, const arma::mat &W, arma::mat &H)
	The update rule for the encoding matrix H. More...

template<typename MatType >
static void	WUpdate (const MatType &V, arma::mat &W, const arma::mat &H)
	The update rule for the basis matrix W. More...

Detailed Description

This class implements a method titled 'Alternating Least Squares' described in the following paper:

@article{paatero1994positive,
 title={Positive matrix factorization: A non-negative factor model with
     optimal utilization of error estimates of data values},
 author={Paatero, P. and Tapper, U.},
 journal={Environmetrics},
 volume={5},
 number={2},
 pages={111--126},
 year={1994}
}

It uses the least squares projection formula to reduce the error value of $\sqrt{\sum_i \sum_j(V-WH)^2}$ by alternately calculating W and H respectively while holding the other matrix constant.

Definition at line 41 of file nmf_als.hpp.

Constructor & Destructor Documentation

mlpack::amf::NMFALSUpdate::NMFALSUpdate ( )

inline

Empty constructor required for the UpdateRule template.

Definition at line 45 of file nmf_als.hpp.

Member Function Documentation

template<typename MatType >

static void mlpack::amf::NMFALSUpdate::HUpdate	(	const MatType &	V,
		const arma::mat &	W,
		arma::mat &	H
	)

inlinestatic

The update rule for the encoding matrix H.

The formula used is

$H = \frac{W^T V}{W^T W}$

The function takes in all the matrices and only changes the value of the H matrix.

Parameters

V	Input matrix to be factorized.
W	Basis matrix.
H	Encoding matrix to be updated.

Definition at line 105 of file nmf_als.hpp.

template<typename MatType >

void mlpack::amf::NMFALSUpdate::Initialize	(	const MatType &	,
		const size_t
	)

inline

Set initial values for the factorization.

In this case, we don't need to set anything.

Definition at line 52 of file nmf_als.hpp.

template<typename Archive >

void mlpack::amf::NMFALSUpdate::Serialize	(	Archive &	,
		const unsigned	int
	)

inline

Serialize the object (in this case, there is nothing to serialize).

Definition at line 123 of file nmf_als.hpp.

template<typename MatType >

static void mlpack::amf::NMFALSUpdate::WUpdate	(	const MatType &	V,
		arma::mat &	W,
		const arma::mat &	H
	)

inlinestatic

The update rule for the basis matrix W.

The formula used isa

$W^T = \frac{H V^T}{H H^T}$

The function takes in all the matrices and only changes the value of the W matrix.

Parameters

V	Input matrix to be factorized.
W	Basis matrix to be updated.
H	Encoding matrix.

Definition at line 72 of file nmf_als.hpp.

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

src/mlpack/methods/amf/update_rules/nmf_als.hpp

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation