NMF Model - Standard model
This class implements the standard model of Nonnegative Matrix Factorization. It provides a general structure and generic functions to manage factorizations that follow the standard NMF model, as defined by Lee et al. (2001).
Let V be a n \times m non-negative matrix and r a positive integer. In its standard form (see references below), a NMF of V is commonly defined as a pair of matrices (W, H) such that:
V \equiv W H,
where:
W and H are n \times r and r \times m matrices respectively with non-negative entries;
\equiv is to be understood with respect to some loss function. Common choices of loss functions are based on Frobenius norm or Kullback-Leibler divergence.
Integer r is called the factorization rank. Depending on the context of application of NMF, the columns of W and H are given different names:
W
basis vector, metagenes, factors, source, image basis
H
mixture coefficients, metagene sample expression profiles, weights
H
basis profiles, metagene expression profiles
NMF approaches have been successfully applied to several fields. The package NMF was implemented trying to use names as generic as possible for objects and methods.
The following terminology is used:
the columns of the target matrix V
the rows of the target matrix V
the first matrix factor W
the columns of first matrix factor W
the second matrix factor H
the columns of second matrix factor H
However, because the package NMF was primarily implemented to work with gene expression microarray data, it also provides a layer to easily and intuitively work with objects from the Bioconductor base framework. See bioc-NMF for more details.
A matrix that contains the basis matrix,
i.e. the first matrix factor of the factorisation
A matrix that contains the coefficient
matrix, i.e. the second matrix factor of the
factorisation
a data.frame that contains the
primary data that define fixed basis terms. See
bterms.
integer vector that contains the indexes of the basis components that are fixed, i.e. for which only the coefficient are estimated.
IMPORTANT: This slot is set on construction of an NMF
model via
nmfModel and
is not recommended to not be subsequently changed by the
end-user.
a data.frame that contains the
primary data that define fixed coefficient terms. See
cterms.
integer vector that contains the indexes of the basis components that have fixed coefficients, i.e. for which only the basis vectors are estimated.
IMPORTANT: This slot is set on construction of an NMF
model via
nmfModel and
is not recommended to not be subsequently changed by the
end-user.
signature(object = "NMFstd"): Get
the basis matrix in standard NMF models
This function returns slot W of object.
signature(object = "NMFstd", value
= "matrix"): Set the basis matrix in standard NMF models
This function sets slot W of object.
signature(object = "NMFstd"):
Default method tries to coerce value into a
data.frame with as.data.frame.
signature(object = "NMFstd"): Get the
mixture coefficient matrix in standard NMF models
This function returns slot H of object.
signature(object = "NMFstd", value =
"matrix"): Set the mixture coefficient matrix in
standard NMF models
This function sets slot H of object.
signature(object = "NMFstd"):
Default method tries to coerce value into a
data.frame with as.data.frame.
signature(object = "NMFstd"):
Compute the target matrix estimate in standard NMF
models.
The estimate matrix is computed as the product of the two
matrix slots W and H:
V ~ W H
signature(object = "NMFstd"):
Method for standard NMF models, which returns the integer
vector that is stored in slot ibterms when a
formula-based NMF model is instantiated.
signature(object = "NMFstd"):
Method for standard NMF models, which returns the integer
vector that is stored in slot icterms when a
formula-based NMF model is instantiated.
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>.
Other NMF-model:
initialize,NMFOffset-method,
NMFns-class, NMFOffset-class
# create a completely empty NMFstd object
new('NMFstd')
# 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)
# create a NMF object based on random (compatible) matrices
p <- 20
h <- rmatrix(r, p)
nmfModel(W=w, H=h)
# create a NMF object based on incompatible matrices: generate an error
h <- rmatrix(r+1, p)
try( new('NMFstd', W=w, H=h) )
try( nmfModel(w, h) )
# Giving target dimensions to the factory method allow for coping with dimension
# incompatibilty (a warning is thrown in such case)
nmfModel(r, W=w, H=h)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.