Related papers: Low-Rank Tensor Recovery via Theta Nuclear p-Norm

Our interest lies in the recoverability properties of compressed tensors under the \textit{canonical polyadic decomposition} (CPD) model. The considered problem is well-motivated in many applications, e.g., hyperspectral image and video…

Present day computers do not have enough memory to store the high-dimensional tensors required when using a direct product basis to compute vibrational energy levels of a polyatomic molecule with more than about 5 atoms. One way to deal…

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…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

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…

We establish several mathematical and computational properties of the nuclear norm for higher-order tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field --- the value of the nuclear norm of a…

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

Low-rank tensor compression has been proposed as a promising approach to reduce the memory and compute requirements of neural networks for their deployment on edge devices. Tensor compression reduces the number of parameters required to…

Higher-order tensors are well-suited for representing multi-dimensional data, such as images and videos, which typically characterize low-rank structures. Low-rank tensor decomposition has become essential in machine learning and computer…

Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem…

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…

This paper studies the rank-$1$ tensor completion problem for cubic tensors. First of all, we show that this problem is equivalent to a special rank-$1$ matrix recovery problem. When the tensor is strongly rank-$1$ completable, we show that…

Weighted nuclear norm minimization has been recently recognized as a technique for reconstruction of a low-rank matrix from compressively sampled measurements when some prior information about the column and row subspaces of the matrix is…

By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…

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…

We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then…

Low-rank tensor methods for the approximate solution of second-order elliptic partial differential equations in high dimensions have recently attracted significant attention. A critical issue is to rigorously bound the error of such…

Low-rank recovery builds upon ideas from the theory of compressive sensing, which predicts that sparse signals can be accurately reconstructed from incomplete measurements. Iterative thresholding-type algorithms-particularly the normalized…

We study the problem of obtaining efficient, deterministic, black-box polynomial identity testing algorithms for depth-3 set-multilinear circuits (over arbitrary fields). This class of circuits has an efficient, deterministic, white-box…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…