mlpack::amf::NMFMultiplicativeDistanceUpdate Class Reference

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

#include <nmf_mult_dist.hpp>

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

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.

Member Function Documentation

HUpdate()

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.

Initialize()

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.

WUpdate()

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.

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

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