Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Document clustering based on non-negative matrix factorization
Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval
Convex Optimization
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Mathematical Programming: Series A and B
Nonsmooth Nonnegative Matrix Factorization (nsNMF)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
Non-negative matrix factorization with α-divergence
Pattern Recognition Letters
SIAM Journal on Matrix Analysis and Applications
On the Complexity of Nonnegative Matrix Factorization
SIAM Journal on Optimization
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
IEEE Transactions on Audio, Speech, and Language Processing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
On the Uniqueness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations
IEEE Transactions on Information Theory
Discriminative Orthogonal Nonnegative matrix factorization with flexibility for data representation
Expert Systems with Applications: An International Journal
Non-negative sparse decomposition based on constrained smoothed ℓ0 norm
Signal Processing
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Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the @?^1-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the @?^0-pseudo-norm. In this paper, we propose a framework for approximate NMF which constrains the @?^0-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches.