Related papers: An Efficient Two-Sided Sketching Method for Large-…

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…

Low-tubal-rank tensor approximation has been proposed to analyze large-scale and multi-dimensional data. However, finding such an accurate approximation is challenging in the streaming setting, due to the limited computational resources. To…

Tensor ring (TR) decomposition is an efficient approach to discover the hidden low-rank patterns for higher-order tensors, and streaming tensors are becoming highly prevalent in real-world applications. In this paper, we investigate how to…

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…

Data tensors of orders 2 and greater are now routinely being generated. These data collections are increasingly huge and growing. Many scientific and medical data tensors are tensor fields (e.g., images, videos, geographic data) in which…

High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive,…

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…

Sketching is a dimensionality reduction technique where one compresses a matrix by linear combinations that are chosen at random. A line of work has shown how to sketch the Hessian to speed up each iteration in a second order method, but…

Convolutional neural networks (CNNs) with deep architectures have substantially advanced the state-of-the-art in computer vision tasks. However, deep networks are typically resource-intensive and thus difficult to be deployed on mobile…

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…

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

In the present work, we propose new tensor Krylov subspace method for ill posed linear tensor problems such as in color or video image restoration. Those methods are based on the tensor-tensor discrete cosine transform that gives fast…

Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The widely used alternating least squares (ALS) method, which solves a sequence of over-determined least squares subproblems, is costly for large and sparse…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

A common approach for compressing large-scale data is through matrix sketching. In this work, we consider the problem of recovering low-rank matrices from two noisy linear sketches using the double sketching scheme discussed in Fazel et al.…

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…

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…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…