Research map / Learning theory and algorithms / Matrix and tensor methods
Non-negative Matrix Factorization under Heavy Noise
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace separability-based NMF with TSVDNMF (dominant NMF assumptions, thresholding + SVD + clustering) | Noisy NMF synthetic data (dominant data) · Dominant data + Gaussian/Multinomial noise, d=n=100, k=10 | l1-residual: outperforms baselines by 27.4% on average in most settings | Helped |
| Use TSVDNMF instead of separable baselines (SPA, ER-SPA, PW-SPA, Gillis-LP) | Separable data with Gaussian noise β=0.5 · Synthetic Gaussian noise | l1-residual: 0.759 vs 0.765 for ER-SPA | Mixed |
| Use TSVDNMF instead of separable baselines under very high multinomial noise | Dominant data + multinomial noise m=10 · Synthetic multinomial noise | l1-residual: 0.017 vs -0.014 for PW-SPA | Helped |
| Use TSVDNMF for clustering instead of provable baselines (SPA, ER-SPA, PW-SPA) | Real text and face datasets clustering · Reuters10, Reuters48, 20NG, TDT-2, Yale | NMI and accuracy: at least 33% NMI improvement on text datasets (paper's claim) | Helped |
| Replace separability with dominant feature/basis assumptions (heavy noise setting) | Reuters48 clustering · Reuters48 NMI | NMI: 0.456 vs 0.363 for PW-SPA (higher), but paper notes comparable to best TSVD in extended baselines | Mixed |
Closest papers by meaning
- Characterizing the Loss Landscape in Non-Negative Matrix Factorization (AAAI 2021 · similarity 0.90)
- An Exterior Method for Nonnegative Matrix Factorization (ICML 2026 · similarity 0.89)
- Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization (NeurIPS 2018 · similarity 0.89)
- Statistically Optimal $K$-means Clustering via Nonnegative Low-rank Semidefinite Programming (ICLR 2024 · similarity 0.86)
- Fast exact recovery of noisy matrix from few entries: the infinity norm approach (NeurIPS 2025 · similarity 0.85)
- Creating Coherence in Federated Non-Negative Matrix Factorization (AAAI 2025 · similarity 0.85)
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