nmf_update.KL.h. NMF 0.23

Description

Multiplicative updates from Lee et al. (2001) for standard Nonnegative Matrix Factorization models V \approx W H, where the distance between the target matrix and its NMF estimate is measured by the Kullback-Leibler divergence.

nmf_update.KL.w and nmf_update.KL.h compute the updated basis and coefficient matrices respectively. They use a C++ implementation which is optimised for speed and memory usage.

nmf_update.KL.w_R and nmf_update.KL.h_R implement the same updates in plain R.

Usage

nmf_update.KL.h(v, w, h, nbterms = 0L, ncterms = 0L, copy = TRUE)

nmf_update.KL.h_R(v, w, h, wh = NULL)

nmf_update.KL.w(v, w, h, nbterms = 0L, ncterms = 0L, copy = TRUE)

nmf_update.KL.w_R(v, w, h, wh = NULL)

Arguments

v: target matrix
w: current basis matrix
h: current coefficient matrix
nbterms: number of fixed basis terms
ncterms: number of fixed coefficient terms
copy: logical that indicates if the update should be made on the original matrix directly (FALSE) or on a copy (TRUE - default). With copy=FALSE the memory footprint is very small, and some speed-up may be achieved in the case of big matrices. However, greater care should be taken due the side effect. We recommend that only experienced users use copy=TRUE.
wh: already computed NMF estimate used to compute the denominator term.

Value

a matrix of the same dimension as the input matrix to update (i.e. w or h). If copy=FALSE, the returned matrix uses the same memory as the input object.

Details

The coefficient matrix (H) is updated as follows:

H_kj <- H_kj ( sum_i [ W_ik V_ij / (WH)_ij ] ) / ( sum_i W_ik )

  
      These updates are used in built-in NMF algorithms KL and
brunet.
  
      The basis matrix (W) is updated as follows:
W_ik <- W_ik ( sum_u [H_kl A_il / (WH)_il ] ) / ( sum_l H_kl )

References

Lee DD and Seung H (2001). "Algorithms for non-negative matrix factorization." _Advances in neural information processing systems_. .

Author

Update definitions by Lee2001. C++ optimised implementation by Renaud Gaujoux.