The multiplicative distance update rules for matrices W and H. More...

Public Member Functions
	NMFMultiplicativeDistanceUpdate ()

template<typename MatType >
void	Initialize (const MatType &, const size_t)
	Initialize 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

The multiplicative distance update rules for matrices W and H.

This follows a method described in the following paper:

@inproceedings{lee2001algorithms,
  title={Algorithms for non-negative matrix factorization},
  author={Lee, D.D. and Seung, H.S.},
  booktitle={Advances in Neural Information Processing Systems 13
      (NIPS 2000)},
  pages={556--562},
  year={2001}
}

This is a multiplicative rule that ensures that the Frobenius norm $\sqrt{\sum_i \sum_j(V-WH)^2}$ is non-increasing between subsequent iterations. Both of the update rules for W and H are defined in this file.

Definition at line 39 of file nmf_mult_dist.hpp.

Constructor & Destructor Documentation

mlpack::amf::NMFMultiplicativeDistanceUpdate::NMFMultiplicativeDistanceUpdate ( )

inline

Definition at line 43 of file nmf_mult_dist.hpp.

Member Function Documentation

template<typename MatType >

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

inlinestatic

The update rule for the encoding matrix H.

The formula used is

$H_{a\mu} \leftarrow H_{a\mu} \frac{(W^T V)_{a\mu}}{(W^T WH)_{a\mu}}$

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 92 of file nmf_mult_dist.hpp.

template<typename MatType >

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

inline

Initialize the factorization.

These update rules hold no information, so the input parameters are ignored.

Definition at line 50 of file nmf_mult_dist.hpp.

template<typename Archive >

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

inline

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

Definition at line 101 of file nmf_mult_dist.hpp.

template<typename MatType >

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

inlinestatic

The update rule for the basis matrix W.

The formula used isa

$W_{ia} \leftarrow W_{ia} \frac{(VH^T)_{ia}}{(WHH^T)_{ia}}$

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 70 of file nmf_mult_dist.hpp.

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

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

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation