Type: Package
Title: Nonnegative Matrix Factorization
Version: 1.0
Date: 2026-01-06
Author: Michail Tsagris [aut, cre]
Maintainer: Michail Tsagris <mtsagris@uoc.gr>
Depends: R (≥ 4.0)
Imports: ClusterR, Matrix, osqp, parallel, quadprog, Rfast, Rfast2, Rglpk, sparcl, stats
Description: Nonnegative matrix factorization (NMF) is a technique to factorize a matrix with nonnegative values into the product of two matrices. Parallel computing is an option to enhance the speed and high-dimensional and large scale (and/or sparse) data are allowed. Relevant papers include: Wang Y. X. and Zhang Y. J. (2012). Nonnegative matrix factorization: A comprehensive review. IEEE Transactions on Knowledge and Data Engineering, 25(6), 1336-1353 <doi:10.1109/TKDE.2012.51> and Kim H. and Park H. (2008). Nonnegative matrix factorization based on alternating nonnegativity constrained least squares and active set method. SIAM Journal on Matrix Analysis and Applications, 30(2), 713-730 <doi:10.1137/07069239X>.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
NeedsCompilation: no
Packaged: 2026-01-07 17:00:39 UTC; mtsag
Repository: CRAN
Date/Publication: 2026-01-09 15:10:02 UTC

Nonnegative Matrix Factorization

Description

Nonnegative matrix factorization (NMF) is implemented.

Details

Package: nnmf
Type: Package
Version: 1.0
Date: 2026-01-05
License: GPL-2

Maintainers

Michail Tsagris <mtsagris@uoc.gr>

Author(s)

Michail Tsagris mtsagris@uoc.gr.

References

Cutler A. and Breiman L. (1994). Archetypal analysis. Technometrics, 36(4): 338–347.

Initialization strategies for the NMF based on the k-means

Description

Initialization strategies for the NMF based on the k-means algorithm.

Usage

init(x, k, bs = 1, veo = FALSE)

Arguments

x

An n \times D numerical matrix with data.

k

The number of lower dimensions. It must be less than the dimensionality of the data, at most D-1.

bs

The batch size in case the user wants to use the mini-batch k-means algorithm. If bs=1, the classical k-means is used.

veo

If the (number of) variables exceed the (number of) observations set this equal to true. In this case, the sparse k-means algorithm of Witten and Tibshirani (2010) is used to initiate the H matrix.

Details

Nonnegative matrix factorization using quadratic programming is performed. The objective function to be minimized is the square of the Frobenius norm.

Value

W

The W matrix, an n \times k matrix with the mapped data.

H

The H matrix, an k \times D matrix.

Z

The reconstructed data, Z = WH.

obj

The reconstruction error, ||x - Z||_F^2.

error

If the argument history was set to TRUE the reconstruction error at each iteration will be performed, otherwise this is NULL.

iters

The number of iterations performed.

runtime

The runtime required by the algorithm.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

References

Alenazi A. and Tsagris M. (2026). Simplicial nonnegative matrix factorization. In preparation.

Witten D. M. and Tibshirani R. (2010). A framework for feature selection in clustering. Journal of the American Statistical Association, 105(490): 713–726.

Cutler A. and Breiman L. (1994). Archetypal analysis. Technometrics, 36(4): 338–347.

See Also

nmf.qp

Examples

x <- as.matrix(iris[, 1:4])
mod <- nmf.qp(x, 2)
plot(mod$W, colour = iris[, 5])

Simplicial NMF minimizing the Manhattan distance

Description

NMF minimizing the Manhattan distance.

Usage

nmf.manh(x, k, W = NULL, H = NULL, k_meds = TRUE,
maxiter = 1000, tol = 1e-6, ncores = 1)

Arguments

x

An n \times D matrix with data. Zero values are allowed.

k

The number of lower dimensions. It must be less than the dimensionality of the data, at most D-1.

W

If you have an initial estimate for W supply it here. Otherwise leave it NULL.

H

If you have an initial estimate for H supply it here, otherwise leave it NULL.

k_meds

If this is TRUE, then the K-medoids algorithm is used to initiate the W and H matrices.

maxiter

The maximum number of iterations allowed.

tol

The tolerance value to terminate the quadratic programming algorithm.

ncores

Do you want the update of W to be performed in parallel? If yes, specify the number of cores to use.

Details

Nonnegative matrix factorization minimizing the Manhattan distance.

Value

W

The W matrix, an n \times k matrix with the mapped data.

H

The H matrix, an k \times D matrix.

Z

The reconstructed data, Z = WH.

obj

The reconstruction error, ||x - Z||_F^2.

error

If the argument history was set to TRUE the reconstruction error at each iteration will be performed, otherwise this is NULL.

iters

The number of iterations performed.

runtime

The runtime required by the algorithm.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

References

Alenazi A. and Tsagris M. (2026). Simplicial nonnegative matrix factorization. In preparation.

Cutler A. and Breiman L. (1994). Archetypal analysis. Technometrics, 36(4): 338–347.

See Also

nmf.qp

Examples

x <- as.matrix(iris[, 1:4])
mod <- nmf.qp(x, 3)
group <- as.numeric(iris[, 5])
plot(mod$W, col = group)

NMF minimizing the Frobenius norm

Description

NMF minimizing the Frobenius norm using quadratic programming.

Usage

nmf.qp(x, k, W = NULL, H = NULL, k_means = TRUE, bs = 1, veo = FALSE, lr_h = 0.1,
maxiter = 1000, tol = 1e-6, ridge = 1e-8, history = FALSE, ncores = 1)

Arguments

x

An n \times D numerical matrix with data.

k

The number of lower dimensions. It must be less than the dimensionality of the data, at most D-1.

W

If you have an initial estimate for W supply it here. Otherwise leave it NULL.

H

If you have an initial estimate for H supply it here, otherwise leave it NULL.

k_means

If this is TRUE, then the K-means algorithm is used to initiate the W and H matrices.

bs

If you use the K-means algorithm for initialization, you may want to use the mini batch K-means if you have millions of observations. In this case, you need to define the number of batches.

veo

If the number of variables excceeds the number of observations set this is equal to TRUE.

lr_h

If veo is TRUE, then the exponentiated gradient descent method is used to update the H matrix. In this case you need to supply the value of the learning rate, which is 0.1 by default.

maxiter

The maximum number of iterations allowed.

tol

The tolerance value to terminate the quadratic programming algorithm.

ridge

A small quantity added in the diagonal of the D matrix.

history

If this is TRUE, the reconstruction error at each iteration is returned.

ncores

Do you want the update of W to be performed in parallel? If yes, specify the number of cores to use.

Details

Nonnegative matrix factorization using quadratic programming is performed. The objective function to be minimized is the square of the Frobenius norm.

Value

W

The W matrix, an n \times k matrix with the mapped data.

H

The H matrix, an k \times D matrix.

Z

The reconstructed data, Z = WH.

obj

The reconstruction error, ||x - Z||_F^2.

error

If the argument history was set to TRUE the reconstruction error at each iteration will be performed, otherwise this is NULL.

iters

The number of iterations performed.

runtime

The runtime required by the algorithm.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

References

Alenazi A. and Tsagris M. (2026). Simplicial nonnegative matrix factorization. In preparation.

Cutler A. and Breiman L. (1994). Archetypal analysis. Technometrics, 36(4): 338–347.

See Also

nmf.sqp

Examples

x <- as.matrix(iris[, 1:4])
mod <- nmf.qp(x, 2)
group <- as.numeric(iris[, 5])
plot(mod$W, col = group)

NMF minimizing the Frobenius norm

Description

NMF minimizing the Frobenius norm using quadratic programming.

Usage

nmf.sqp(x, k, W = NULL, H = NULL, maxiter = 1000, tol = 1e-4, ridge = 1e-8,
history = FALSE, ncores = 1)

Arguments

x

An n \times D dgC class sparse matrix with data.

k

The number of lower dimensions. It must be less than the dimensionality of the data, at most D-1.

W

If you have an initial estimate for W supply it here. Otherwise leave it NULL.

H

If you have an initial estimate for H supply it here, otherwise leave it NULL.

maxiter

The maximum number of iterations allowed.

tol

The tolerance value to terminate the quadratic programming algorithm. The value is set to 1e-4 in this case because with large scale and/or sparse data the computation time is really high. So, we sacrifice some accuracy over speed.

ridge

A small quantity added in the diagonal of the D matrix.

history

If this is TRUE, the reconstruction error at each iteration is returned.

ncores

Do you want the update of W to be performed in parallel? If yes, specify the number of cores to use.

Details

Nonnegative matrix factorization using quadratic programming is performed. The objective function to be minimized is the square of the Frobenius norm. This function is suitable for large scale sparse data, and parallel computing is a must in this case. Note that we do not use k-means here and that the reconstruced matrix Z is not returned with this function for capacity purposes.

Value

W

The W matrix, an n \times k matrix with the mapped data.

H

The H matrix, an k \times D matrix.

obj

The reconstruction error, ||x - Z||_F^2.

error

If the argument history was set to TRUE the reconstruction error at each iteration will be performed, otherwise this is NULL.

iters

The number of iterations performed.

runtime

The runtime required by the algorithm.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

References

Alenazi A. and Tsagris M. (2026). Simplicial nonnegative matrix factorization. In preparation.

Cutler A. and Breiman L. (1994). Archetypal analysis. Technometrics, 36(4): 338–347.

See Also

nmf.qp

Examples

x <- as.matrix(iris[, 1:4])
mod <- nmf.qp(x, 2)
group <- as.numeric(iris[, 5])
plot(mod$W, col = group)