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_R`

and `nmf_update.KL.h_R`

implement the same updates in *plain R*.

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.

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.

`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 )

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