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Subhayan Saha (Universite de Mons)5/18/26, 3:45 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
Minimum-volume nonnegative matrix factorization (min-vol NMF) has been used successfully in many applications, such as hyperspectral imaging, chemical kinetics, spectroscopy, topic modeling, and audio source separation. However, its robustness to noise has been a long-standing open problem. In this paper, we prove that min-vol NMF identifies the groundtruth factors in the presence of noise...
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Stefano Sicilia (University of Mons)5/18/26, 4:10 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
Given a matrix $X$, and two ranks $r_1$ and $r_2$, the Hadamard decomposition (HD) consists in looking for two low-rank matrices, $X_1$ of rank $r_1$ and $X_2$ of rank $r_2$, both of the same size as $X$, such that $X\approx X_1\circ X_2$, where $\circ$ is the Hadamard (element-wise) product. HD is more expressive than standard low-rank approximations, such as the truncated singular value...
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Damjana Kokol Bukovšek (University of Ljubljana)5/18/26, 4:35 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
We consider a symmetric nonnegative matrix $A$ of order $n \times n$. A factorization of the form $A = BCB^T$, where $B$ is a nonnegative matrix of order $n \times k$ and $C$ is a symmetric nonnegative matrix of order $k \times k$, is called symmetric nonnegative trifactorization (SNT for short) of $A$. Minimal possible $k$ in such factorization is called the SNT-rank of $A$.
The...
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Dr Alberto Bucci (University of Edinburgh)5/18/26, 5:00 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
In this work, we present the tree tensor network Nyström (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker or tensor-train formats, to the more general tree tensor network format, enabling a unified treatment of various existing methods. Our method retains the key features of the generalized Nyström approximation for matrices, i.e. it is...
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Charlotte Vermeylen (KU Leuven)5/19/26, 2:00 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
A novel optimization framework is proposed for solving the low-rank tensor approximation problem using the canonical polyadic decomposition (CPD). This can be a difficult optimization problem for certain tensors, e.g., due to degeneracy, i.e., a tensor that can be approximated arbitrarily closely by an ill-conditioned tensor of lower rank. This is one of the phenomena that are encountered in...
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David Thorsteinsson (KU Leuven)5/19/26, 2:25 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
Block term decomposition (BTD) unifies the two most common tensor decompositions: canonical polyadic and Tucker. While BTDs have found a broad range of applications from machine learning to blind source separation, all known algorithms for computing BTDs were historically optimisation-based, and required the desired block sizes to be specified as input. Recently, algebraic BTD algorithms have...
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Alberto Bucci (University of Edinburgh)5/19/26, 2:50 PMLow-rank Matrix and Tensor Decompositions: Theory, Algorithms and ApplicationsMinisymposium Talk
We present a new technique for efficiently compressing matrix–vector products in the tensor-train (TT) format, avoiding the explicit formation of intermediate tensors arising from standard MPO–MPS multiplication. The proposed method performs the compression in a single pass, leading to significant computational and memory savings.
From a theoretical point of view, the resulting...
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