Using underapproximations for sparse nonnegative matrix factorization
Pattern Recognition
A multilevel approach for nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Sparse nonnegative matrix factorization with ℓ0-constraints
Neurocomputing
Computing a nonnegative matrix factorization -- provably
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons
SIAM Journal on Scientific Computing
Low-Rank Matrix Approximation with Weights or Missing Data Is NP-Hard
SIAM Journal on Matrix Analysis and Applications
Perturbation of Matrices and Nonnegative Rank with a View toward Statistical Models
SIAM Journal on Matrix Analysis and Applications
Computing the Stationary Distribution of a Finite Markov Chain Through Stochastic Factorization
SIAM Journal on Matrix Analysis and Applications
Lifts of Convex Sets and Cone Factorizations
Mathematics of Operations Research
An information complexity approach to extended formulations
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Sparse and unique nonnegative matrix factorization through data preprocessing
The Journal of Machine Learning Research
Discovering relations using matrix factorization methods
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Most Tensor Problems Are NP-Hard
Journal of the ACM (JACM)
An upper bound for nonnegative rank
Journal of Combinatorial Theory Series A
Subtractive clustering for seeding non-negative matrix factorizations
Information Sciences: an International Journal
Approximate aggregation of Markovian models using alternating least squares
Performance Evaluation
Journal of Global Optimization
Nonnegative rank factorization--a heuristic approach via rank reduction
Numerical Algorithms
Global convergence of modified multiplicative updates for nonnegative matrix factorization
Computational Optimization and Applications
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Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases, and other information retrieval and clustering applications. The problem is most naturally posed as continuous optimization. In this report, we define an exact version of NMF. Then we establish several results about exact NMF: (i) that it is equivalent to a problem in polyhedral combinatorics; (ii) that it is NP-hard; and (iii) that a polynomial-time local search heuristic exists.