Running NMF algorithms
The function nmf is a S4 generic defines the main
interface to run NMF algorithms within the framework
defined in package NMF. It has many methods that
facilitates applying, developing and testing NMF
algorithms.
The package vignette vignette('NMF') contains an
introduction to the interface, through a sample data
analysis.
nmf(x, rank, method, ...)
## S4 method for signature 'matrix,numeric,NULL'
nmf(x, rank, method,
seed = NULL, model = NULL, ...)
## S4 method for signature 'matrix,numeric,list'
nmf(x, rank, method, ...,
.parameters = list())
## S4 method for signature 'matrix,numeric,function'
nmf(x, rank, method,
seed, model = "NMFstd", ..., name,
objective = "euclidean", mixed = FALSE)
## S4 method for signature 'matrix,NMF,ANY'
nmf(x, rank, method, seed,
...)
## S4 method for signature 'matrix,NULL,ANY'
nmf(x, rank, method, seed,
...)
## S4 method for signature 'matrix,matrix,ANY'
nmf(x, rank, method, seed,
model = list(), ...)
## S4 method for signature 'formula,ANY,ANY'
nmf(x, rank, method, ...,
model = NULL)
## S4 method for signature 'matrix,numeric,NMFStrategy'
nmf(x, rank,
method, seed = nmf.getOption("default.seed"),
rng = NULL, nrun = if (length(rank) > 1) 30 else 1,
model = NULL, .options = list(),
.pbackend = nmf.getOption("pbackend"),
.callback = NULL, ...)x |
target data to fit, i.e. a matrix-like object |
rank |
specification of the factorization rank. It
is usually a single numeric value, but other type of
values are possible (e.g. matrix), for which specific
methods are implemented. See for example methods
If |
method |
specification of the NMF algorithm. The
most common way of specifying the algorithm is to pass
the access key (i.e. a character string) of an algorithm
stored in the package's dedicated registry, but methods
exists that handle other types of values, such as
If Cases where the algorithm is inferred from the call are
when an NMF model is passed in arguments |
... |
extra arguments to allow extension of the
generic. Arguments that are not used in the chain of
internal calls to |
.parameters |
list of method-specific parameters.
Its elements must have names matching a single method
listed in |
name |
name associated with the NMF algorithm
implemented by the function |
objective |
specification of the objective function
associated with the algorithm implemented by the function
It may be either |
mixed |
a logical that indicates if the algorithm
implemented by the function |
seed |
specification of the starting point or seeding method, which will compute a starting point, usually using data from the target matrix in order to provide a good guess. The seeding method may be specified in the following way:
|
rng |
rng specification for the run(s). This argument should be used to set the the RNG seed, while still specifying the seeding method argument seed. |
model |
specification of the type of NMF model to use. It is used to instantiate the object that inherits from
class
Argument/slot conflicts: In the case a parameter
of the algorithm has the same name as a model slot, then
If a variable appears in both arguments |
nrun |
number of runs to perform. It specifies the
number of runs to perform. By default only one run is
performed, except if When using a random seeding method, multiple runs are generally required to achieve stability and avoid bad local minima. |
.options |
this argument is used to set runtime options. It can be a The string must be composed of characters that correspond
to a given option (see mapping below), and modifiers '+'
and '-' that toggle options on and off respectively. E.g.
Modifiers '+' and '-' apply to all option character found
after them: for options that accept integer values, the value may be
appended to the option's character e.g. The following options are available (the characters after
“-” are those to use to encode
|
.pbackend |
specification of the
Currently it accepts the following values:
|
.callback |
Used when option The call is wrapped into a tryCatch so that callback errors do not stop the whole computation (see below). The results of the different calls to the callback
function are stored in a miscellaneous slot accessible
using the method If no error occurs See the examples for sample code. |
The nmf function has multiple methods that compose
a very flexible interface allowing to:
combine NMF algorithms with seeding methods and/or stopping/convergence criterion at runtime;
perform multiple NMF runs, which are computed in parallel whenever the host machine allows it;
run multiple algorithms with a common set of parameters, ensuring a consistent environment (notably the RNG settings).
The workhorse method is
nmf,matrix,numeric,NMFStrategy, which is
eventually called by all other methods. The other methods
provides convenient ways of specifying the NMF
algorithm(s), the factorization rank, or the seed to be
used. Some allow to directly run NMF algorithms on
different types of objects, such as data.frame or
ExpressionSet objects.
The returned value depends on the run mode:
signature(x = "data.frame", rank =
"ANY", method = "ANY"): Fits an NMF model on a
data.frame.
The target data.frame is coerced into a matrix
with as.matrix.
signature(x = "matrix", rank =
"numeric", method = "NULL"): Fits an NMF model using an
appropriate algorithm when method is not supplied.
This method tries to select an appropriate algorithm
amongst the NMF algorithms stored in the internal
algorithm registry, which contains the type of NMF models
each algorithm can fit. This is possible when the type of
NMF model to fit is available from argument seed,
i.e. if it is an NMF model itself. Otherwise the
algorithm to use is obtained from
nmf.getOption('default.algorithm').
This method is provided for internal usage, when called
from other nmf methods with argument method
missing in the top call (e.g.
nmf,matrix,numeric,missing).
signature(x = "matrix", rank =
"numeric", method = "list"): Fits multiple NMF models on
a common matrix using a list of algorithms.
The models are fitted sequentially with nmf using
the same options and parameters for all algorithms. In
particular, irrespective of the way the computation is
seeded, this method ensures that all fits are performed
using the same initial RNG settings.
This method returns an object of class
NMFList, that is essentially a list
containing each fit.
signature(x = "matrix", rank =
"numeric", method = "character"): Fits an NMF model on
x using an algorithm registered with access key
method.
Argument method is partially match against the
access keys of all registered algorithms (case
insensitive). Available algorithms are listed in section
Algorithms below or the introduction vignette. A
vector of their names may be retrieved via
nmfAlgorithm().
signature(x = "matrix", rank =
"numeric", method = "function"): Fits an NMF model on
x using a custom algorithm defined the function
method.
The supplied function must have signature
(x=matrix, start=NMF, ...) and return an object
that inherits from class NMF. It
will be called internally by the workhorse nmf
method, with an NMF model to be used as a starting point
passed in its argument start.
Extra arguments in ... are passed to method
from the top nmf call. Extra arguments that have
no default value in the definition of the function
method are required to run the algorithm (e.g. see
argument alpha of myfun in the examples).
If the algorithm requires a specific type of NMF model,
this can be specified in argument model that is
handled as in the workhorse nmf method (see
description for this argument).
signature(x = "matrix", rank = "NMF",
method = "ANY"): Fits an NMF model using the NMF model
rank to seed the computation, i.e. as a starting
point.
This method is provided for convenience as a shortcut for
nmf(x, nbasis(object), method, seed=object, ...)
It discards any value passed in argument seed and
uses the NMF model passed in rank instead. It
throws a warning if argument seed not missing.
If method is missing, this method will call the
method nmf,matrix,numeric,NULL, which will infer
an algorithm suitable for fitting an NMF model of the
class of rank.
signature(x = "matrix", rank = "NULL",
method = "ANY"): Fits an NMF model using the NMF model
supplied in seed, to seed the computation, i.e. as
a starting point.
This method is provided for completeness and is
equivalent to nmf(x, seed, method, ...).
signature(x = "matrix", rank =
"missing", method = "ANY"): Method defined to ensure the
correct dispatch to workhorse methods in case of argument
rank is missing.
signature(x = "matrix", rank =
"numeric", method = "missing"): Method defined to ensure
the correct dispatch to workhorse methods in case of
argument method is missing.
signature(x = "matrix", rank = "matrix",
method = "ANY"): Fits an NMF model partially seeding the
computation with a given matrix passed in rank.
The matrix rank is used either as initial value
for the basis or mixture coefficient matrix, depending on
its dimension.
Currently, such partial NMF model is directly used as a seed, meaning that the remaining part is left uninitialised, which is not accepted by all NMF algorithm. This should change in the future, where the missing part of the model will be drawn from some random distribution.
Amongst built-in algorithms, only ‘snmf/l’ and ‘snmf/r’ support partial seeds, with only the coefficient or basis matrix initialised respectively.
signature(x = "matrix", rank =
"data.frame", method = "ANY"): Shortcut for nmf(x,
as.matrix(rank), method, ...).
signature(x = "formula", rank = "ANY",
method = "ANY"): This method implements the interface
for fitting formula-based NMF models. See
nmfModel.
Argument rank target matrix or formula
environment. If not missing, model must be a
list, a data.frame or an environment
in which formula variables are searched for.
Lee and Seung's multiplicative updates are used by several NMF algorithms. To improve speed and memory usage, a C++ implementation of the specific matrix products is used whenever possible. It directly computes the updates for each entry in the updated matrix, instead of using multiple standard matrix multiplication.
The algorithms that benefit from this optimization are: 'brunet', 'lee', 'nsNMF' and 'offset'. However there still exists plain R versions for these methods, which implement the updates as standard matrix products. These are accessible by adding the prefix '.R#' to their name: '.R#brunet', '.R#lee', '.R#nsNMF' and '.R#offset'.
All algorithms are accessible by their respective access key as listed below. The following algorithms are available:
Standard NMF, based on the Kullback-Leibler divergence, from Brunet et al. (2004). It uses simple multiplicative updates from Lee et al. (2001), enhanced to avoid numerical underflow.
Default stopping criterion: invariance of the
connectivity matrix (see
nmf.stop.connectivity).
Standard NMF based on the Euclidean distance from Lee et al. (2001). It uses simple multiplicative updates.
Default stopping criterion: invariance of the
connectivity matrix (see
nmf.stop.connectivity).
Least-Square NMF from Wang et al. (2006). It uses modified versions of Lee and Seung's multiplicative updates for the Euclidean distance, which incorporates weights on each entry of the target matrix, e.g. to reflect measurement uncertainty.
Default stopping criterion: stationarity of the objective
function (see nmf.stop.stationary).
Nonsmooth NMF from Pascual-Montano et al. (2006). It uses a modified version of Lee and Seung's multiplicative updates for the Kullback-Leibler divergence Lee et al. (2001), to fit a extension of the standard NMF model, that includes an intermediate smoothing matrix, meant meant to produce sparser factors.
Default stopping criterion: invariance of the
connectivity matrix (see
nmf.stop.connectivity).
NMF with offset from Badea (2008). It uses a modified version of Lee and Seung's multiplicative updates for Euclidean distance Lee et al. (2001), to fit an NMF model that includes an intercept, meant to capture a common baseline and shared patterns, in order to produce cleaner basis components.
Default stopping criterion: invariance of the
connectivity matrix (see
nmf.stop.connectivity).
Pattern-Expression NMF from Zhang2008. It uses multiplicative updates to minimize an objective function based on the Euclidean distance, that is regularized for effective expression of patterns with basis vectors.
Default stopping criterion: stationarity of the objective
function (see nmf.stop.stationary).
Alternating
Least Square (ALS) approach from Kim et al. (2007). It
applies the nonnegative least-squares algorithm from
Van Benthem et al. (2004) (i.e. fast combinatorial
nonnegative least-squares for multiple right-hand), to
estimate the basis and coefficient matrices alternatively
(see fcnnls). It minimises an
Euclidean-based objective function, that is regularized
to favour sparse basis matrices (for ‘snmf/l’) or
sparse coefficient matrices (for ‘snmf/r’).
Stopping criterion: built-in within the internal
workhorse function nmf_snmf, based on the KKT
optimality conditions.
The purpose of seeding methods is to compute initial values for the factor matrices in a given NMF model. This initial guess will be used as a starting point by the chosen NMF algorithm.
The seeding method to use in combination with the
algorithm can be passed to interface nmf through
argument seed. The seeding seeding methods
available in registry are listed by the function
nmfSeed (see list therein).
Detailed examples of how to specify the seeding method and its parameters can be found in the Examples section of this man page and in the package's vignette.
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\#0>.
Wang G, Kossenkov AV and Ochs MF (2006). "LS-NMF: a modified non-negative matrix factorization algorithm utilizing uncertainty estimates." _BMC bioinformatics_, *7*, pp. 175. ISSN 1471-2105, <URL: http://dx.doi.org/10.1186/1471-2105-7-175>, <URL: http://www.ncbi.nlm.nih.gov/pubmed/16569230>.
Pascual-Montano A, Carazo JM, Kochi K, Lehmann D and Pascual-marqui RD (2006). "Nonsmooth nonnegative matrix factorization (nsNMF)." _IEEE Trans. Pattern Anal. Mach. Intell_, *28*, pp. 403-415.
Badea L (2008). "Extracting gene expression profiles common to colon and pancreatic adenocarcinoma using simultaneous nonnegative matrix factorization." _Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing_, *290*, pp. 267-78. ISSN 1793-5091, <URL: http://www.ncbi.nlm.nih.gov/pubmed/18229692>.
Kim H and Park H (2007). "Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis." _Bioinformatics (Oxford, England)_, *23*(12), pp. 1495-502. ISSN 1460-2059, <URL: http://dx.doi.org/10.1093/bioinformatics/btm134>, <URL: http://www.ncbi.nlm.nih.gov/pubmed/17483501>.
Van Benthem M and Keenan MR (2004). "Fast algorithm for the solution of large-scale non-negativity-constrained least squares problems." _Journal of Chemometrics_, *18*(10), pp. 441-450. ISSN 0886-9383, <URL: http://dx.doi.org/10.1002/cem.889>, <URL: http://doi.wiley.com/10.1002/cem.889>.
# Only basic calls are presented in this manpage.
# Many more examples are provided in the demo file nmf.R
## Not run:
demo('nmf')
## End(Not run)
# random data
x <- rmatrix(20,10)
# run default algorithm with rank 2
res <- nmf(x, 2)
# specify the algorithm
res <- nmf(x, 2, 'lee')
# get verbose message on what is going on
res <- nmf(x, 2, .options='v')
## Not run:
# more messages
res <- nmf(x, 2, .options='v2')
# even more
res <- nmf(x, 2, .options='v3')
# and so on ...
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.