NMF: nmf_update_KL – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

nmf_update_KL

NMF Multiplicative Updates for Kullback-Leibler Divergence

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.

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 )

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.

Author(s)

Update definitions by Lee2001.

C++ optimised implementation by Renaud Gaujoux.

References

Lee DD and Seung H (2001). "Algorithms for non-negative matrix factorization." _Advances in neural information processing systems_. <URL: http://scholar.google.com/scholar?q=intitle:Algorithms+for+non-negative+matrix+factorization\#0>.

NMF

Algorithms and Framework for Nonnegative Matrix Factorization (NMF)

v0.23.0

GPL (>= 2)

Authors

Renaud Gaujoux, Cathal Seoighe

Initial release

2020-07-30