Nonnegative Matrix Factorization in the Component-Wise L1 Norm for Sparse Data

arXiv:2603.29715 · cs.LG, eess.SP, math.OC, stat.ML · Submitted 2026-03-31 · Read on arXiv

cs.LG, eess.SP, math.OC, stat.ML

Submitted: 2026-03-31

Updated: 2026-09-18

Comments: 23 pages before supplementary, code available from https://github.com/giovanniseraghiti/wL1-NMF

Code: https://github.com/giovanniseraghiti/wL1-NMF

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Sparsity — 31× in this paper · explained in 4 episodes
• Interpretability — 5× in this paper · explained in 15 episodes
• Matrix Completion — 4× in this paper · explained in 4 episodes
• Conference on Computer Vision and Pattern Recognition — 3× in this paper
• Generalization — 3× in this paper · explained in 13 episodes
• Nesterov Smoothing — 3× in this paper
• Objective Function — 3× in this paper · explained in 2 episodes
• Regularization — 3× in this paper · explained in 3 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Convergence Guarantees — 2× in this paper · explained in 3 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Computational Biology — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Feature Extraction — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• MahNMF: Manhattan Non-negative Matrix Factorization
• Projected subgradient methods for paraconvex optimization: Application to robust low-rank matrix recovery

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