The built-in NMF algorithms described here minimise the
Kullback-Leibler divergence (KL) between an NMF model and
a target matrix. They use the updates for the basis and
coefficient matrices (`W`

and `H`

) defined by
Brunet et al. (2004), which are essentially those
from Lee et al. (2001), with an stabilisation step
that shift up all entries from zero every 10 iterations,
to a very small positive value.

`nmf_update.brunet`

implements in C++ an optimised
version of the single update step.

Algorithms ‘brunet’ and ‘.R#brunet’ provide
the complete NMF algorithm from Brunet et al.
(2004), using the C++-optimised and pure R updates
`nmf_update.brunet`

and
`nmf_update.brunet_R`

respectively.

Algorithm ‘KL’ provides an NMF algorithm based on
the C++-optimised version of the updates from
Brunet et al. (2004), which uses the stationarity
of the objective value as a stopping criterion
`nmf.stop.stationary`

, instead of the
stationarity of the connectivity matrix
`nmf.stop.connectivity`

as used by
‘brunet’.

```
file.show(system.file('matlab', 'brunet.m',
package='NMF'))
```

nmf_update.brunet_R(i, v, x, eps = .Machine$double.eps, ...) nmf_update.brunet(i, v, x, copy = FALSE, eps = .Machine$double.eps, ...) nmfAlgorithm.brunet_R(..., .stop = NULL, maxIter = 2000, eps = .Machine$double.eps, stopconv = 40, check.interval = 10) nmfAlgorithm.brunet(..., .stop = NULL, maxIter = 2000, copy = FALSE, eps = .Machine$double.eps, stopconv = 40, check.interval = 10) nmfAlgorithm.KL(..., .stop = NULL, maxIter = 2000, copy = FALSE, eps = .Machine$double.eps, stationary.th = .Machine$double.eps, check.interval = 5 * check.niter, check.niter = 10L) nmfAlgorithm.brunet_M(..., object, y, x)

- i
- current iteration number.
- v
- target matrix.
- x
- current NMF model, as an
`NMF-class`

object. - eps
- small numeric value used to ensure numeric stability, by shifting up entries from zero to this fixed value.
- ...
- extra arguments. These are generally not used
and present only to allow other arguments from the main
call to be passed to the initialisation and stopping
criterion functions (slots
`onInit`

and`Stop`

respectively). - 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`

. - .stop
- specification of a stopping criterion, that
is used instead of the one associated to the NMF
algorithm. It may be specified as:
- the access key of a registered stopping criterion;
- a
single integer that specifies the exact number of
iterations to perform, which will be honoured unless a
lower value is explicitly passed in argument
`maxIter`

. - a single numeric value that
specifies the stationnarity threshold for the objective
function, used in with
`nmf.stop.stationary`

; - a function with signature
`(object="NMFStrategy", i="integer", y="matrix", x="NMF", ...)`

, where`object`

is the`NMFStrategy`

object that describes the algorithm being run,`i`

is the current iteration,`y`

is the target matrix and`x`

is the current value of the NMF model.

- maxIter
- maximum number of iterations to perform.
- object
- an object computed using some algorithm, or that describes an algorithm itself.
- y
- data object, e.g. a target matrix
- stopconv
- number of iterations intervals over which the connectivity matrix must not change for stationarity to be achieved.
- check.interval
- interval (in number of iterations) on which the stopping criterion is computed.
- stationary.th
- maximum absolute value of the gradient, for the objective function to be considered stationary.
- check.niter
- number of successive iteration used to compute the stationnary criterion.

Original MATLAB files and references can be found at:

http://www.broadinstitute.org/mpr/publications/projects/NMF/nmf.m

http://www.broadinstitute.org/publications/broad872

Original license terms:

This software and its documentation are copyright 2004 by the Broad Institute/Massachusetts Institute of Technology. All rights are reserved. This software is supplied without any warranty or guaranteed support whatsoever. Neither the Broad Institute nor MIT can not be responsible for its use, misuse, or functionality.

`nmf_update.brunet_R`

implements in pure R a single
update step, i.e. it updates both matrices.

Brunet J, Tamayo P, Golub TR and Mesirov JP (2004).
"Metagenes and molecular pattern discovery using matrix
factorization." _Proceedings of the National Academy of
Sciences of the United States of America_, *101*(12), pp.
4164-9. ISSN 0027-8424,

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