nmf_update_KL: NMF Multiplicative Updates for Kullback-Leibler Divergence

In NMF: Algorithms and Framework for Nonnegative Matrix Factorization (NMF)

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} \leftarrow H_{kj} \frac{\left( sum_i \frac{W_{ik} V_{ij}}{(WH)_{ij}} \right)}{ 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} \leftarrow W_{ik} \frac{ sum_j [\frac{H_{kj} A_{ij}}{(WH)_{ij}} ] }{sum_j H_{kj} }

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>.

NMF documentation built on Sept. 11, 2024, 8:34 p.m.