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This paper presents an exact and explicit tensor-network equation for the search of nontrivial divisors of a composite integer, together with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which…

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multi-way data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner…

The online analysis of multi-way data stored in a tensor $\mathcal{X} \in \mathbb{R} ^{I_1 \times \dots \times I_N} $ has become an essential tool for capturing the underlying structures and extracting the sensitive features which can be…

In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals…

A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…

Image Segmentation is one of the core tasks in Computer Vision and solving it often depends on modeling the image appearance data via the color distributions of each it its constituent regions. Whereas many segmentation algorithms handle…

We consider the Principal Component Analysis problem for large tensors of arbitrary order $k$ under a single-spike (or rank-one plus noise) model. On the one hand, we use information theory, and recent results in probability theory, to…

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…

In the last decades, tensors have emerged as the right tool to represent multidimensional data in a compact yet informative manner. Moreover, it is well-known that by performing low-rank factorizations of such tensors one is often able to…

Tensor-based modulation (TBM) has been proposed in the context of unsourced random access for massive uplink communication. In this modulation, transmitters encode data as rank-1 tensors, with factors from a discrete vector constellation.…

The factorization of three-dimensional data continues to gain attention due to its relevance in representing and compressing large-scale datasets. The linear-map-based tensor-tensor multiplication is a matrix-mimetic operation that extends…

Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have…

We study a monostatic multiple-input multiple-output sensing scenario assisted by a reconfigurable intelligent surface using tensor signal modeling. We propose a method that exploits the intrinsic multidimensional structure of the received…

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…

Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…