Related papers: Reconstruction Algorithms for Low-Rank Tensors and…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…
Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
In this paper, we focus on the fixed TT-rank and precision problems of finding an approximation of the tensor train (TT) decomposition of a tensor. Note that the TT-SVD and TT-cross are two well-known algorithms for these two problems.…
Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component…
Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{Tensor power method} (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor…
Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…
A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of…
An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…
There has been continued interest in seeking a theorem describing optimal low-rank approximations to tensors of order 3 or higher, that parallels the Eckart-Young theorem for matrices. In this paper, we argue that the naive approach to this…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
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…
Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of…
Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a semi-definite program algorithm for computing the maximum $H$-eigenvalue of a…
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…