Nonsmooth nonnegative matrix factorization (nsNMF)

By Alberto Domingo Pascual-Montano, J. M. Carazo, Kieko Kochi, Dietrich Lehmann, Roberto D. Pascual-Marqui. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006

427 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Genetics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/5b82d8b2c7dcb6d46f02a9de0a5b791b50889333

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Citations in the corpus

Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing (2009, methodology): “1) nsNMF: The method proposed in [29] introduces a “smoothing” matrix C ∈ RP×P into the original NMF model (5)”
Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization (2011, background): “In general, the L1 regularizer is the most popular choice for achieving sparsity of the abundance matrix [26], [27], [28].”
Nonnegative Matrix Factorization: A Comprehensive Review (2013, neutral): “In fact this is identical to the previous work of Nonsmooth NMF (NSNMF) [115], where the incorporation of a very smooth factor SS makes UU and VV quite sparse, and thus reconciles the contradiction between approximation and sparseness.”
Endmember Extraction From Highly Mixed Data Using Minimum Volume Constrained Nonnegative Matrix Factorization (2007, background): “For many applications, the nonuniqueness of solution can be alleviated by adding additional constraints to confine the feasible solution set, such as the smoothness constraint [18] for better spectral signatures, the sparseness constraint [22], and the nonsmoothness constraint [26] for part-based st”
A survey of dimensionality reduction techniques (2014, background): “Non ‐ smooth NMF [Pascual ‐ Montano2006] modifies the NMF factorization to .”
A flexible R package for nonnegative matrix factorization (2010, methodology): “Some variations on equation (1) and the optimization problem (2) are possible, depending on the application field or the a priori knowledge one has of the observed data [12,13].”
Nonnegative Matrix Factorization Based on Alternating Nonnegativity Constrained Least Squares and Active Set Method (2008, background): “Several approaches [7, 14, 28, 29] have been proposed to explicitly control the degree of sparseness in the factors of the NMF.”