Related papers: An O(1) Space Algorithm for N-Dimensional Tensor R…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to…

We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in…

Tensors serve as a crucial tool in the representation and analysis of complex, multi-dimensional data. As data volumes continue to expand, there is an increasing demand for developing optimization algorithms that can directly operate on…

Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random…

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…

Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…

The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…

We give an explicit plane-by-plane filtered back-projection reconstruction algorithm for the transverse ray transform of symmetric second rank tensor fields on Euclidean 3-space, using data from rotation about three orthogonal axes. We show…

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…

A well known numerical task is the inversion of large symmetric tridiagonal Toeplitz matrices, i.e., matrices whose entries equal $a$ on the diagonal and $b$ on the extra diagonals ($a, b\in \mathbb R$). The inverses of such matrices are…

We extend our previous work on a semi-Lagrangian adaptive rank (SLAR) integrator, in the finite difference framework for nonlinear Vlasov-Poisson systems, to the general high-order tensor setting. The proposed scheme retains the high-order…

A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration…

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…

Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…

Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…

In this paper we derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First we decompose the manifold via 1+1+2 semi-tetrad formalism that yields a…

In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product…

Tensor operations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we establish a few basic properties of the range and null space of a tensor using block circulant…