nmf_update_KL: NMF Multiplicative Updates for Kullback-Leibler Divergence
In renozao/NMF: Algorithms and Framework for Nonnegative Matrix Factorization (NMF)

Description Usage Arguments Details Value Author(s) References

Multiplicative updates from Lee and Seung (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.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)

`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.

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.

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 )

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.

Update definitions by Lee2001.

C++ optimised implementation by Renaud Gaujoux.

Lee DD, 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>.

renozao/NMF documentation built on June 14, 2020, 9:35 p.m.