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

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  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>.

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