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’.
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 = nmf.getOption("maxIter") %||% 2000,
eps = .Machine$double.eps, stopconv = 40,
check.interval = 10)
nmfAlgorithm.brunet(..., .stop = NULL,
maxIter = nmf.getOption("maxIter") %||% 2000,
copy = FALSE, eps = .Machine$double.eps, stopconv = 40,
check.interval = 10)
nmfAlgorithm.KL(..., .stop = NULL,
maxIter = nmf.getOption("maxIter") %||% 2000,
copy = FALSE, eps = .Machine$double.eps,
stationary.th = .Machine$double.eps,
check.interval = 5 * check.niter, check.niter = 10L)
current iteration number.
target matrix.
current NMF model, as an
NMF object.
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).
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.
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.
maximum number of iterations to perform.
number of iterations intervals over which the connectivity matrix must not change for stationarity to be achieved.
interval (in number of iterations) on which the stopping criterion is computed.
maximum absolute value of the gradient, for the objective function to be considered stationary.
number of successive iteration used to compute the stationnary criterion.
Original implementation in MATLAB: Jean-Philippe Brunet brunet@broad.mit.edu
Port to R and optimisation in C++: Renaud Gaujoux
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, <URL: http://dx.doi.org/10.1073/pnas.0308531101>, <URL: http://www.ncbi.nlm.nih.gov/pubmed/15016911>.
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>.