arXiv Machine Learning
Aug 27
Maximum-Volume Nonnegative Matrix Factorization
arXiv:2602. 04795v3 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) is a popular data embedding technique.
A Provably-Correct and Robust Convex Model for Smooth Separable NMF
arXiv:2511. 07109v2 Announce Type: replace-cross Abstract: Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling.
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arXiv Machine Learning
Sep 21
Nonnegative Matrix Factorization in the Component-Wise L1 Norm for Sparse Data
arXiv:2603.29715v2 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, X, by the product of two nonnegative factors, WH, where W has r columns a...
arXiv Machine Learning
Jul 16
An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence
arXiv:2607. 13919v1 Announce Type: new Abstract: Nonnegative Matrix Factorization (NMF) is a fundamental tool in unsupervised learning, which approximates a nonnegative matrix by the product of two low-rank nonnegative factors.
arXiv Machine Learning
Sep 1
Separable Nonnegative Matrix Factorization Using Powered Ratio-of-Norms Regularization
arXiv:2608.28799v1 Announce Type: cross Abstract: Separable nonnegative matrix factorization (SNMF) has been widely used for low-rank representation and clustering of nonnegative data, owing to its a...
arXiv Machine Learning
Jun 9
On solving symmetric multi-type orthogonal non-negative matrix tri-factorization problem
arXiv:2606. 08291v1 Announce Type: new Abstract: We study the symmetric multi-type orthogonal non-negative matrix tri-factorization problem, where several symmetric non-negative matrices are simultaneously approximated by factors of the form $GS_{i}G^{\top}$, with a shared non-negative and orthogonal factor $G$.
arXiv Machine Learning
Jun 19
Alternating Direction Method of Multipliers for Nonlinear Matrix Decompositions
arXiv:2512. 17473v3 Announce Type: replace-cross Abstract: We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD).
arXiv Machine Learning
Jun 3
A Nonmonotone Gradient-Based Algorithm for Symmetric Nonnegative Matrix Factorization and Graph Clustering
arXiv:2606. 02887v1 Announce Type: new Abstract: Symmetric nonnegative matrix factorization (Symmetric NMF) approximates a matrix as $WW^T$ with nonnegative rectangular factor $W$.
arXiv Machine Learning
Jul 31
Sparsity Induced Identifiability in Matrix Tri-Factorisation
arXiv:2607. 27507v1 Announce Type: new Abstract: Matrix factorisation is a fundamental tool for exploiting low-dimensional structure in high-dimensional data, with applications such as data compression, denoising, structure discovery, interpretable representation learning, and dimensionality reduction.
arXiv Computer Vision
Sep 21
MultiHU-TD: Multifeature Hyperspectral Unmixing Based on Tensor Decomposition
The paper introduces MultiHU‑TD, an interpretable framework for multifeature hyperspectral unmixing that employs tensor decomposition and incorporates the abundance sum‑to‑one constraint via an ADMM algorithm. It extends previous models by adding mathematical morphology and neighborhood patch analysis, and provides detailed mathematical, physical, and graphical interpretations linked to the extended linear mixing model. Experiments on real hyperspectral images demonstrate the model’s interpretability and effectiveness, with code released on GitHub.
arXiv Machine Learning
Aug 11
Understanding Alternating Minimization for Matrix Completion
arXiv:1312. 0925v4 Announce Type: replace Abstract: Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems.
arXiv Machine Learning
Jul 23
Non--negative matrix factorization using the \textit{R} package \textsf{nnmf}
arXiv:2607. 20084v1 Announce Type: cross Abstract: Non--negative matrix factorization (NMF) has become an established dimensionality reduction technique for extracting latent structures from non--negative data and has found widespread applications in fields such as bioinformatics, text mining, image analysis, and recommender systems.
Hugging Face Trending Papers
Sep 10
Identifiability of Nonnegative Tensor Decompositions via Positive Scattering
The paper introduces a new concept called positive scattering to enhance identifiability of nonnegative tensor decompositions. By combining this scattering term with existing dimension-based conditions, the authors derive two sufficient criteria that guarantee minimality, nonnegative rank, and uniqueness for subsets of components. The key result is a positive splitting inequality that links dimension constraints with support-induced geometric rigidity, and the authors show that the scattering term’s mode costs are discrete, enabling an exact activation characterization via graph connectivity. This criterion can certify sparse nonnegative tensor decompositions that elude traditional Kruskal and Lovitz–Petrov conditions, even after reshaping, and reduces to familiar matrix results in the two-dimensional case.