nmf.manh: Simplicial NMF minimizing the Manhattan distance

Description

NMF minimizing the Manhattan distance.

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

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.

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.

Michail Tsagris.

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

Nonnegative matrix factorization minimizing the Manhattan distance.

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.

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

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