Nonnegative matrix factorization for spectral data analysis

By V. P. Pauca, Johathan Piper, Robert J. Plemmons. 2006

649 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Biomedical Engineering, Media Technology

View Paper: https://www.semanticscholar.org/paper/50a66ada68ded1a8908f623e93a447b78ea37b81

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In Analytical Chemistry

In Biomedical Engineering

In Media Technology

Citations in the corpus

Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis (2007, background): “…two non-negative matrices W 2 Rm k and H 2 Rk n so that A WH: ð1Þ A solution to the NMF problem can be obtained by solving the following optimization problem: min W,H f ðW,HÞ 1 2 kA WHk2F, s:t: W,H 0, ð2Þ where W 2 Rm k is a basis matrix, H 2 Rk n is a coefficient matrix, k kF is the Frobenius…”
Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework (2013, background): “Over the last decade, 26 NMF has received enormous attention and has been successfully applied to a broad range 27 of important problems in areas including text mining [77,85], computer vision [47,69], 28 bioinformatics [10,23,52], spectral data analysis [76], and blind source separation [22] among ”
Feature dimensionality reduction: a review (2022, methodology): “In addition, the use of astronomical spectrometers is to analyze data [75].”
Algorithms for Nonnegative Matrix Factorization with the β-Divergence (2010, result): “Hence the nonnegativity constraint may become active and must be treated carefully; in that case our result coincides with similar ﬁndings of Pauca et al. (2006); Mørup and Clemmensen (2007) for the speciﬁc case of ℓ 1 -regularized NMF with the Euclidean distance ( β = 2).”
Recommender Systems (2016, neutral): “This results in a modification [474] of the update equations as follows:”
Endmember Extraction From Highly Mixed Data Using Minimum Volume Constrained Nonnegative Matrix Factorization (2007, methodology): “Considering the low convergence of SCNMF, we allow the maximum number of iteration to be 300.”
Nonnegative Matrix Factorization Based on Alternating Nonnegativity Constrained Least Squares and Active Set Method (2008, methodology): “FIG. 6.2. The values of vs. the number of iterations for SNMF/R [18] with and CNMF based on multiplicative update rules [ 30 ] with and on the leukemia ALLAML data set with . We used the KKT convergence criterion with .”
Multi-view clustering: A survey (2018, positive): “The reconstruction processes[126] can be formulated as a Frobenius norm optimization problem, defined as min W;H kX WHk2F; s.t., W > 0;H > 0 (12) Moreover, many variants of NMF have also been put forward, such as G-orthogonal NMF[127], Regularized NMF[128, 129], Convex and Semi-NMF[130], and Multila”
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons (2011, background): “On the other hand, when W and H are not necessarily of full column rank, a regularized formulation may be considered [17, 29]:”
Coupled Nonnegative Matrix Factorization Unmixing for Hyperspectral and Multispectral Data Fusion (2012, methodology): “Over the last decade, nonnegative matrix factorization (NMF) [31], [32] has emerged as a useful unmixing method [27]–[30].”
Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization (2011, methodology): “Nonnegative matrix factorization (NMF) [16], [17], which decomposes the data into two nonnegative matrices, is a natural solution to the nonnegativity constraint [18].”
K-SVD and its non-negative variant for dictionary design (2005, background): “Application for NMF are many and include dimensionality reduction [17] and analysis of data such as audio [18], text [19] and even data obtained from astronomical spectrometers [20].”
Manifold Regularized Sparse NMF for Hyperspectral Unmixing (2013, background): “Nonnegative sparse coding [20] incorporates sparse coding as sparsity constraint into NMF, whereas smoothness constraint is considered in [21].”
Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing (2009, methodology): “The computation time of CNMF, PSnsNMF, and PSNMFSC has no obvious difference.”