Nonnegative Matrix Factorization Based on Alternating Nonnegativity Constrained Least Squares and Active Set Method

By Hyunsoo Kim, Haesun Park. SIAM Journal on Matrix Analysis and Applications, 2008

623 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/55d0e5e82095ce4f9a79591221c3a8bdc78e3ac1

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Citations in the corpus

Symmetric Nonnegative Matrix Factorization for Graph Clustering (2012, methodology): “NMF: We use the alternating nonnegative least squares algorithm [11] to obtain a solution of the standard form of NMF (1.”
Ieee Transactions on Pattern Analysis and Machine Intelligence Laplacian Regularized Low-rank Representation and Its Applications (neutral): “To introduce richer information over Z, people consider imposing some helpful regularization on the coefficient matrix, such as sparsity [15] [43] and a non-negative constraint [23].”
Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework (2013, methodology): “The active-set method [53,64] does not require the full-rank condition as long as a zero vector is used for initialization [28].”
Generalized Low Rank Models (2014, methodology): “Hence a number of specialized algorithms and codes for fitting NNMF models are available [86, 91, 78, 80, 13, 79, 81].”
Low-rank matrix completion using alternating minimization (2012, methodology): “For example, clustering [16], sparse PCA [25], non-negative matrix factorization [15], signed network prediction [9] etc.”
The Why and How of Nonnegative Matrix Factorization (2014, methodology): “…(ANLS) is a class of methods where the subproblems in W and H are solved exactly, that is, the update for W is given by Many methods can be used to solve the NNLS argmin W ≥ 0 || X − W H || F , and dedicated active-set methods have shown to perform very well in practice 6 ; see [72, 73, 75].”
Pure component spectral recovery and constrained matrix factorizations: concepts and applications (2010, methodology): “[11, 13, 14, 15] using the implementation [12] and theNonnegative matrix factorization/Alternating Nonnegativity Constrained Least Squares(NMF/ANLS) algorithm of Kim and Park [16].”
Alternating Back-Propagation for Generator Network (2016, methodology): “…learning, such as alternating linear regression in the EM algorithm for factor analysis, alternating least squares algorithm for matrix factorization (Koren, Bell, and Volinsky, 2009; Kim and Park, 2008), and alternating gradient descent algorithm for sparse coding (Olshausen and Field, 1997).”
Outlier Detection for Text Data (2017, methodology): “H≥0f(W (k+1),H). (7) Since thesub-problemsare non-negativityconstrained least squares (NLS) problems, the two-block BCD method has been called thealternating non-negativeleast square (ANLS) framework [26, 19, 20]. 3.1.2 BCDwith 2k VectorBlocks- HALS/RRIMethod We partition the unknowns into 2k blocks”
On Tensors, Sparsity, and Nonnegative Factorizations (2011, neutral): “Much of the past work in nonnegative matrix and tensor analysis has focused on the LS error [44, 43, 6, 20, 26, 25, 23, 17, 27], which corresponds D ow nl oa de d 01 /0 2/ 13 to 1 98 .”
Recommender Systems (2016, neutral): “Details of the alternating least-squares method for non-negative matrix factorization may be found in [161, 301].”
NeNMF: An Optimal Gradient Method for Nonnegative Matrix Factorization (2012, background): “B. Yuan is with Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240 China (e-mail: boyuan@sjtu.edu.cn).”
Blitz: A Principled Meta-Algorithm for Scaling Sparse Optimization (2015, methodology): “More broadly, working sets have been applied successfully to a diverse set of optimization problems involving sparsity or constraints; see Fan et al. (2005), Tsochantaridis et al. (2005), and Kim & Park (2008) as examples.”
A fast polygon inflation algorithm to compute the area of feasible solutions for three‐component systems. I: concepts and applications (2013, methodology): “This can be performed by standard factorization tools such as the PCD code [15] or by the MCR-ANLS algorithm [29], the SPECFIT code [30], or even by the NNMF code [26] written in MATLAB.”
A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion (2013, methodology): “The ANLS methods in [30,32] are extended to solving (1.”
Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems (2016, background): “Nevertheless, the solution in (7) has already offered a globally optimal solution to the counterpart design problem at the receiver side.”
Provable Alternating Gradient Descent for Non-negative Matrix Factorization with Strong Correlations (2017, neutral): “We compare the algorithm AND to the following popular methods: Alternating Non-negative Least Square ( ANLS (Kim & Park, 2008)), multiplicative update ( MU (Lee & Seung, 2001)), LDA (online version (Hoffman et al., 2010)), 7 and Hierarchical Alternating Least Square ( HALS (Cichocki et al., 2007)).”
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons (2011, methodology): “Their multiplicative updating algorithm [23] has been one of the most commonly used for NMF, but some issues related to its performance [24, 15, 17] and problems with convergence [11] were reported.”
Phase Retrieval Using Alternating Minimization (2013, background): “In particular, if m ≥ C 1 n log 3 n for large enough C 1 > 0, then whp we have (cid:107) x 0 − x ∗ 2 ≤ 1 / 100 (or any other constant).”