NMF: dot-fcnnls – R documentation

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dot-fcnnls

Internal Routine for Fast Combinatorial Nonnegative Least-Squares

Description

This is the workhorse function for the higher-level function fcnnls, which implements the fast nonnegative least-square algorithm for multiple right-hand-sides from Van Benthem et al. (2004) to solve the following problem:

min ||Y - X K||_F, s.t. K>=0

where Y and X are two real matrices of dimension n x p and n x r respectively, and |.|_F is the Frobenius norm.

The algorithm is very fast compared to other approaches, as it is optimised for handling multiple right-hand sides.

Usage

.fcnnls(x, y, verbose = FALSE, pseudo = FALSE, eps = 0)

Arguments

`x`	the coefficient matrix
`y`	the target matrix to be approximated by X K.
`verbose`	logical that indicates if log messages should be shown.
`pseudo`	By default (`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.
`eps`	threshold for considering entries as nonnegative. This is an experimental parameter, and it is recommended to leave it at 0.

Value

A list with the following elements:

`coef`	the fitted coefficient matrix.
`Pset`	the set of passive constraints, as a logical matrix of the same size as `K` that indicates which element is positive.

References

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>.

NMF

Algorithms and Framework for Nonnegative Matrix Factorization (NMF)

v0.23.0

GPL (>= 2)

Authors

Renaud Gaujoux, Cathal Seoighe

Initial release

2020-07-30