This function solves the following nonnegative least square linear problem using normal equations and the fast combinatorial strategy from Van Benthem et al. (2004):
min ||Y - X K||_F, s.t. K>=0where
YandXare two real matrices of dimensionn x pandn x rrespectively, and|.|_Fis the Frobenius norm.The algorithm is very fast compared to other approaches, as it is optimised for handling multiple right-hand sides.
fcnnls(x, y, ...)
S4 (matrix,matrix)
`fcnnls`(x, y, verbose = FALSE, pseudo = TRUE, ...)
.fcnnls.
Currently not used.FALSE).X K.pseudo=FALSE) the algorithm uses Gaussian
elimination to solve the successive internal linear problems, using the
solve function. If pseudo=TRUE the algorithm uses
Moore-Penrose generalized pseudoinverse from the
corpcor package instead of solve.A list containing the following components:
x the estimated optimal matrix K. fitted the fitted
matrix X K. residuals the residual matrix Y - X K.
deviance the residual sum of squares between the fitted matrix
X K and the target matrix Y. That is the sum of the square
residuals. passive a r x p logical matrix containing the
passive set, that is the set of entries in K that are not null (i.e.
strictly positive). pseudo a logical that is TRUE if the
computation was performed using the pseudoinverse. See argument
pseudo.
Within the NMF package, this algorithm is used internally by the
SNMF/R(L) algorithm from Kim et al. (2007) to solve general Nonnegative
Matrix Factorization (NMF) problems, using alternating nonnegative
constrained least-squares.
That is by iteratively and alternatively estimate each matrix factor.
The algorithm is an active/passive set method, which rearrange the
right-hand side to reduce the number of pseudo-inverse calculations.
It uses the unconstrained solution K_u obtained from the
unconstrained least squares problem,
i.e. min ||Y - X K||_F^2 , so as to determine
the initial passive sets.
The function fcnnls is provided separately so that it can be
used to solve other types of nonnegative least squares problem.
For faster computation, when multiple nonnegative least square fits
are needed, it is recommended to directly use the function .fcnnls.
The code of this function is a port from the original MATLAB code provided by Kim et al. (2007).
signature(x = "matrix", y = "matrix"): This method wraps a call to the internal function .fcnnls, and
formats the results in a similar way as other lest-squares methods such
as lm.
signature(x = "numeric", y = "matrix"): Shortcut for fcnnls(as.matrix(x), y, ...).
signature(x = "ANY", y = "numeric"): Shortcut for fcnnls(x, as.matrix(y), ...).
Original MATLAB code from Van Benthem and Keenan, slightly modified by H. Kim: http://www.cc.gatech.edu/~hpark/software/fcnnls.m
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,
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,
## Define a random nonnegative matrix matrix
n <- 200; p <- 20; r <- 3
V <- rmatrix(n, p)
## Compute the optimal matrix K for a given X matrix
X <- rmatrix(n, r)
res <- fcnnls(X, V)
## Compute the same thing using the Moore-Penrose generalized pseudoinverse
res <- fcnnls(X, V, pseudo=TRUE)
## It also works in the case of single vectors
y <- runif(n)
res <- fcnnls(X, y)
# or
res <- fcnnls(X[,1], y)
nmf