mlpack::amf::NMFALSUpdate Class Reference

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

#include <nmf_als.hpp>

Public Member Functions
	NMFALSUpdate ()
	Empty constructor required for the UpdateRule template.
template<typename MatType >
void	Initialize (const MatType &, const size_t)
	Set initial values for the factorization. More...
template<typename Archive >
void	serialize (Archive &, const uint32_t)
	Serialize the object (in this case, there is nothing to serialize).

Static Public Member Functions
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...
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...

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.

Member Function Documentation

HUpdate()

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.

Initialize()

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.

WUpdate()

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.

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

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