Related papers: Tensor-decomposition techniques for ab initio nucl…

Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…

Accurate and fast treatment of electron-electron interactions remains a central challenge in electronic structure theory because post-Hartree-Fock methods often suffered from the computational cost for 4-index electron repulsion integrals…

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity…

We study the problem of low-rank tensor factorization in the presence of missing data. We ask the following question: how many sampled entries do we need, to efficiently and exactly reconstruct a tensor with a low-rank orthogonal…

Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing…

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

Recent theoretical investigations of two-body hadronic B decays have provided justification for the use of the factorization ansatz to evaluate the B decay matrix elements. Motivated by this, we present simplified formulae for a wide range…

Tensor decompositions are a fundamental tool in scientific computing and data analysis. In many applications -- such as simulation data on irregular grids, surrogate modeling for parameterized PDEs, or spectroscopic measurements -- the data…

Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…

Tensor-oriented multi-view subspace clustering has achieved significant strides in assessing high-order correlations and improving clustering analysis of multi-view data. Nevertheless, most of existing investigations are typically hampered…

The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC…

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system"…

Two-body reduced density matrices (2RDMs) encode the essential two-electron physics of electronic states, but their quartic storage cost poses a major limitation in practical workflows. We investigate a simple protocol to compress both…

Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…