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.
arXiv:2609. 11606v1 Announce Type: cross Abstract: Identifiability of tensor decompositions is often established through linear-algebraic conditions on the factor families.
arXiv:2602. 04795v3 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) is a popular data embedding technique.
arXiv:2609.14307v1 Announce Type: new Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, u...
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.
arXiv:2606. 04176v1 Announce Type: new Abstract: We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar.
arXiv:2609.09258v1 Announce Type: new Abstract: We present a method for recovering the moral graph of a causal DAG from a probability distribution over discrete variables, using fully connected tenso...
The paper applies parameterised graph theory to tensor networks, showing that cutwidth and tree‑cutwidth bound the bond‑dimension overhead needed to represent a tensor‑network state as a matrix product state or tree tensor network. It derives graph‑dependent upper bounds on the sample and computational complexity of tensor‑network tomography, introducing a new graph parameter called learning complexity. Finally, it extends the framework to an agnostic learner that approximates any state with a tensor‑network state of given bond dimension, providing explicit graph‑dependent complexity bounds.
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:2602. 05869v2 Announce Type: replace-cross Abstract: We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion.
arXiv:2606. 15679v1 Announce Type: cross Abstract: Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products.
arXiv:2608. 08642v1 Announce Type: new Abstract: We study exact Kullback--Leibler (KL) projection for low-rank factorizations whose two nonnegative factors have prescribed row marginals and a shared, learned column marginal.
arXiv:2603.02720v2 Announce Type: replace Abstract: Recently, tensor decompositions have attracted increasing attention. Fundamentally, different interactions among factors induce distinct tensor dec...