`nmfModel`

is a S4 generic function which provides a
convenient way to build NMF models. It implements a
unified interface for creating `NMF`

objects from
any NMF models, which is designed to resolve potential
dimensions inconsistencies.

`nmfModels`

lists all available NMF models currently
defined that can be used to create NMF objects, i.e. --
more or less -- all S4 classes that inherit from class
`NMF-class`

.

nmfModel(rank, target = 0L, ...) S4 (numeric,numeric) `nmfModel`(rank, target, ncol = NULL, model = "NMFstd", W, H, ..., force.dim = TRUE, order.basis = TRUE) S4 (numeric,matrix) `nmfModel`(rank, target, ..., use.names = TRUE) S4 (formula,ANY) `nmfModel`(rank, target, ..., data = NULL, no.attrib = FALSE) nmfModels(builtin.only = FALSE)

- rank
- specification of the target factorization rank (i.e. the number of components).
- target
- an object that specifies the dimension of the estimated target matrix.
- ...
- extra arguments to allow extension, that are
passed down to the workhorse method
`nmfModel,numeric.numeric`

, where they are used to initialise slots specific to the instantiating NMF model class. - ncol
- a numeric value that specifies the number of
columns of the target matrix, fitted the NMF model. It is
used only if not missing and when argument
`target`

is a single numeric value. - model
- the class of the object to be created. It
must be a valid class name that inherits from class
`NMF`

. Default is the standard NMF model`NMFstd-class`

. - W
- value for the basis matrix.
`data.frame`

objects are converted into matrices with`as.matrix`

. - H
- value for the mixture coefficient matrix
`data.frame`

objects are converted into matrices with`as.matrix`

. - force.dim
- logical that indicates whether the method should try lowering the rank or shrinking dimensions of the input matrices to make them compatible
- order.basis
- logical that indicates whether the basis components should reorder the rows of the mixture coefficient matrix to match the order of the basis components, based on their respective names. It is only used if the basis and coefficient matrices have common unique column and row names respectively.
- use.names
- a logical that indicates whether the dimension names of the target matrix should be set on the returned NMF model.
- data
- Optional argument where to look for the variables used in the formula.
- no.attrib
- logical that indicate if attributes
containing data related to the formula should be attached
as attributes. If
`FALSE`

attributes`'target'`

and`'formula'`

contain the target matrix, and a list describing each formula part (response, regressors, etc.). - builtin.only
- logical that indicates whether only built-in NMF models, i.e. defined within the NMF package, should be listed.

All `nmfModel`

methods return an object that
inherits from class `NMF`

, that is suitable for
seeding NMF algorithms via arguments `rank`

or
`seed`

of the `nmf`

method, in which
case the factorisation rank is implicitly set by the
number of basis components in the seeding model (see
`nmf`

).

For convenience, shortcut methods and internal
conversions for working on `data.frame`

objects
directly are implemented. However, note that conversion
of a `data.frame`

into a `matrix`

object may
take some non-negligible time, for large datasets. If
using this method or other NMF-related methods several
times, consider converting your data `data.frame`

object into a matrix once for good, when first loaded.

- nmfModel
`signature(rank = "numeric", target = "numeric")`

: Main factory method for NMF modelsThis method is the workhorse method that is eventually called by all other methods. See section

*Main factory method*for more details. - nmfModel
`signature(rank = "numeric", target = "missing")`

: Creates an empty NMF model of a given rank.This call is equivalent to

`nmfModel(rank, 0L, ...)`

, which creates*empty*`NMF`

object with a basis and mixture coefficient matrix of dimension 0 x`rank`

and`rank`

x 0 respectively. - nmfModel
`signature(rank = "missing", target = "ANY")`

: Creates an empty NMF model of null rank and a given dimension.This call is equivalent to

`nmfModel(0, target, ...)`

. - nmfModel
`signature(rank = "NULL", target = "ANY")`

: Creates an empty NMF model of null rank and given dimension.This call is equivalent to

`nmfModel(0, target, ...)`

, and is meant for internal usage only. - nmfModel
`signature(rank = "missing", target = "missing")`

: Creates an empty NMF model or from existing factorsThis method is equivalent to

`nmfModel(0, 0, ..., force.dim=FALSE)`

. This means that the dimensions of the NMF model will be taken from the optional basis and mixture coefficient arguments`W`

and`H`

. An error is thrown if their dimensions are not compatible.Hence, this method may be used to generate an NMF model from existing factor matrices, by providing the named arguments

`W`

and/or`H`

:`nmfModel(W=w)`

or`nmfModel(H=h)`

or`nmfModel(W=w, H=h)`

Note that this may be achieved using the more convenient interface is provided by the method

`nmfModel,matrix,matrix`

(see its dedicated description).See the description of the appropriate method below.

- nmfModel
`signature(rank = "numeric", target = "matrix")`

: Creates an NMF model compatible with a target matrix.This call is equivalent to

`nmfModel(rank, dim(target), ...)`

. That is that the returned NMF object fits a target matrix of the same dimension as`target`

.Only the dimensions of

`target`

are used to construct the`NMF`

object. The matrix slots are filled with`NA`

values if these are not specified in arguments`W`

and/or`H`

. However, dimension names are set on the return NMF model if present in`target`

and argument`use.names=TRUE`

. - nmfModel
`signature(rank = "matrix", target = "matrix")`

: Creates an NMF model based on two existing factors.This method is equivalent to

`nmfModel(0, 0, W=rank, H=target..., force.dim=FALSE)`

. This allows for a natural shortcut for wrapping existing**compatible**matrices into NMF models: nmfModel(w, h)Note that an error is thrown if their dimensions are not compatible.

- nmfModel
`signature(rank = "data.frame", target = "data.frame")`

: Same as`nmfModel('matrix', 'matrix')`

but for`data.frame`

objects, which are generally produced by`read.delim`

-like functions.The input

`data.frame`

objects are converted into matrices with`as.matrix`

. - nmfModel
`signature(rank = "matrix", target = "ANY")`

: Creates an NMF model with arguments`rank`

and`target`

swapped.This call is equivalent to

`nmfModel(rank=target, target=rank, ...)`

. This allows to call the`nmfModel`

function with arguments`rank`

and`target`

swapped. It exists for convenience:- allows typing
`nmfModel(V)`

instead of`nmfModel(target=V)`

to create a model compatible with a given matrix`V`

(i.e. of dimension`nrow(V), 0, ncol(V)`

) - one can pass the arguments in any order (the one that comes to the user's mind first) and it still works as expected.

- allows typing
- nmfModel
`signature(rank = "formula", target = "ANY")`

: Build a formula-based NMF model, that can incorporate fixed basis or coefficient terms.

The main factory engine of NMF models is implemented by
the method with signature `numeric, numeric`

. Other
factory methods provide convenient ways of creating NMF
models from e.g. a given target matrix or known
basis/coef matrices (see section *Other Factory
Methods*).

This method creates an object of class `model`

,
using the extra arguments in `...`

to initialise
slots that are specific to the given model.

All NMF models implement get/set methods to access the
matrix factors (see `basis`

), which are
called to initialise them from arguments `W`

and
`H`

. These argument names derive from the definition
of all built-in models that inherit derive from class
`NMFstd-class`

, which has two slots, `W`
and `H`, to hold the two factors -- following the
notations used in Lee et al. (1999).

If argument `target`

is missing, the method creates
a standard NMF model of dimension 0x`rank`

x0. That
is that the basis and mixture coefficient matrices,
`W` and `H`, have dimension 0x`rank`

and
`rank`

x0 respectively.

If target dimensions are also provided in argument
`target`

as a 2-length vector, then the method
creates an `NMF`

object compatible to fit a target
matrix of dimension `target[1]`

x`target[2]`

.
That is that the basis and mixture coefficient matrices,
`W` and `H`, have dimension
`target[1]`

x`rank`

and
`rank`

x`target[2]`

respectively. The target
dimensions can also be specified using both arguments
`target`

and `ncol`

to define the number of
rows and the number of columns of the target matrix
respectively. If no other argument is provided, these
matrices are filled with NAs.

If arguments `W`

and/or `H`

are provided, the
method creates a NMF model where the basis and mixture
coefficient matrices, `W` and `H`, are
initialised using the values of `W`

and/or `H`

.

The dimensions given by `target`

, `W`

and
`H`

, must be compatible. However if
`force.dim=TRUE`

, the method will reduce the
dimensions to the achieve dimension compatibility
whenever possible.

When `W`

and `H`

are both provided, the
`NMF`

object created is suitable to seed a NMF
algorithm in a call to the `nmf`

method. Note
that in this case the factorisation rank is implicitly
set by the number of basis components in the seed.

Lee DD and Seung HS (1999). "Learning the parts of
objects by non-negative matrix factorization." _Nature_,
*401*(6755), pp. 788-91. ISSN 0028-0836,

```
# data
n <- 20; r <- 3; p <- 10
V <- rmatrix(n, p) # some target matrix
# create a r-ranked NMF model with a given target dimensions n x p as a 2-length vector
nmfModel(r, c(n,p)) # directly
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 3
## samples: 10
```

```
nmfModel(r, dim(V)) # or from an existing matrix <=> nmfModel(r, V)
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 3
## samples: 10
```

```
# or alternatively passing each dimension separately
nmfModel(r, n, p)
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 3
## samples: 10
```

```
# trying to create a NMF object based on incompatible matrices generates an error
w <- rmatrix(n, r)
h <- rmatrix(r+1, p)
try( new('NMFstd', W=w, H=h) )
try( nmfModel(w, h) )
try( nmfModel(r+1, W=w, H=h) )
# The factory method can be force the model to match some target dimensions
# but warnings are thrown
nmfModel(r, W=w, H=h)
```

```
## Warning: nmfModel - Objective rank [3] is lower than the number of rows in
## H [4]: only the first 3 rows of H will be used
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 3
## samples: 10
```

```
nmfModel(r, n-1, W=w, H=h)
```

```
## Warning: nmfModel - Number of rows in target is lower than the number of
## rows in W [20]: only the first 19 rows of W will be used Warning: nmfModel
## - Objective rank [3] is lower than the number of rows in H [4]: only the
## first 3 rows of H will be used
```

```
## <Object of class:NMFstd>
## features: 19
## basis/rank: 3
## samples: 10
```

```
## Empty model of given rank
nmfModel(3)
```

```
## <Object of class:NMFstd>
## features: 0
## basis/rank: 3
## samples: 0
```

```
nmfModel(target=10) #square
```

```
## <Object of class:NMFstd>
## features: 10
## basis/rank: 0
## samples: 10
```

```
nmfModel(target=c(10, 5))
```

```
## <Object of class:NMFstd>
## features: 10
## basis/rank: 0
## samples: 5
```

```
# Build an empty NMF model
nmfModel()
```

```
## <Object of class:NMFstd>
## features: 0
## basis/rank: 0
## samples: 0
```

```
# create a NMF object based on one random matrix: the missing matrix is deduced
# Note this only works when using factory method NMF
n <- 50; r <- 3;
w <- rmatrix(n, r)
nmfModel(W=w)
```

```
## <Object of class:NMFstd>
## features: 50
## basis/rank: 3
## samples: 0
```

```
# create a NMF object based on random (compatible) matrices
p <- 20
h <- rmatrix(r, p)
nmfModel(H=h)
```

```
## <Object of class:NMFstd>
## features: 0
## basis/rank: 3
## samples: 20
```

```
# specifies two compatible matrices
nmfModel(W=w, H=h)
```

```
## <Object of class:NMFstd>
## features: 50
## basis/rank: 3
## samples: 20
```

```
# error if not compatible
try( nmfModel(W=w, H=h[-1,]) )
# create a r-ranked NMF model compatible with a given target matrix
obj <- nmfModel(r, V)
all(is.na(basis(obj)))
```

```
## [1] TRUE
```

```
## From two existing factors
# allows a convenient call without argument names
w <- rmatrix(n, 3); h <- rmatrix(3, p)
nmfModel(w, h)
```

```
## <Object of class:NMFstd>
## features: 50
## basis/rank: 3
## samples: 20
```

```
# Specify the type of NMF model (e.g. 'NMFns' for non-smooth NMF)
mod <- nmfModel(w, h, model='NMFns')
mod
```

```
## <Object of class:NMFns>
## features: 50
## basis/rank: 3
## samples: 20
## theta: 0.5
```

```
# One can use such an NMF model as a seed when fitting a target matrix with nmf()
V <- rmatrix(mod)
res <- nmf(V, mod)
nmf.equal(res, nmf(V, mod))
```

```
## [1] TRUE
```

```
# NB: when called only with such a seed, the rank and the NMF algorithm
# are selected based on the input NMF model.
# e.g. here rank was 3 and the algorithm "nsNMF" is used, because it is the default
# algorithm to fit "NMFns" models (See ?nmf).
## swapped arguments `rank` and `target`
V <- rmatrix(20, 10)
nmfModel(V) # equivalent to nmfModel(target=V)
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 0
## samples: 10
```

```
nmfModel(V, 3) # equivalent to nmfModel(3, V)
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 3
## samples: 10
```

```
# empty 3-rank model
nmfModel(~ 3)
```

```
## <Object of class:NMFstd>
## features: 0
## basis/rank: 3
## samples: 0
```

```
# 3-rank model that fits a given data matrix
x <- rmatrix(20,10)
nmfModel(x ~ 3)
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 3
## samples: 10
```

```
# add fixed coefficient term defined by a factor
gr <- gl(2, 5)
nmfModel(x ~ 3 + gr)
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 5
## samples: 10
## fixed coef [2]:
## gr = <1, 2>
```

```
# add fixed coefficient term defined by a numeric covariate
nmfModel(x ~ 3 + gr + b, data=list(b=runif(10)))
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 6
## samples: 10
## fixed coef [3]:
## gr = <1, 2>
## b = 0.316867901943624, 0.381737500894815, ..., 0.50038011232391
```

```
# 3-rank model that fits a given ExpressionSet (with fixed coef terms)
e <- ExpressionSet(x)
pData(e) <- data.frame(a=runif(10))
nmfModel(e ~ 3 + gr + a) # `a` is looked up in the phenotypic data of x pData(x)
```

```
## <Object of class:NMFstd>
## features: 20
## basis/rank: 6
## samples: 10
## fixed coef [3]:
## gr = <1, 2>
## a = 0.051527991425246, 0.965822806349024, ..., 0.536786474753171
```

```
# show all the NMF models available (i.e. the classes that inherit from class NMF)
nmfModels()
```

```
## [1] "NMFstd" "NMFOffset" "NMFns"
```

```
# show all the built-in NMF models available
nmfModels(builtin.only=TRUE)
```

```
## [1] "NMFstd" "NMFOffset" "NMFns"
```

```
```

`is.empty.nmf`

Other NMF-interface: `basis`

,
`.basis`

, `.basis<-`

,
`basis<-`

, `coef`

,
`.coef`

, `.coef<-`

,
`coef<-`

, `coefficients`

,
`.DollarNames,NMF-method`

,
`loadings,NMF-method`

, `misc`

,
`NMF-class`

, `$<-,NMF-method`

,
`$,NMF-method`

, `rnmf`

,
`scoef`