Related papers: Alignment and matching tests for high-dimensional …

The problem of testing whether a signal lies within a given subspace, also named matched subspace detection, has been well studied when the signal is represented as a vector. However, the matched subspace detection methods based on vectors…

Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…

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…

Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…

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…

This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…

We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…

Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based…

Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…

Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…

Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…

Copositivity of tensors plays an important role in vacuum stability of a general scalar potential, polynomial optimization, tensor complementarity problem and tensor generalized eigenvalue complementarity problem. In this paper, we propose…