Related papers: Tensor CUR Decomposition under the Linear-Map-Base…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized canonical polyadic (GCP) low-rank tensor…

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…

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors).…

The CUR matrix decomposition is an important extension of Nystr\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR…

We determine the structure of linear maps on the tensor product of matrices which preserve the numerical range or numerical radius.

We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization…

The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…

Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…

Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…

Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described…

One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…

Tensor decomposition has proven to be a strong tool in various 3D image processing tasks such as denoising and super-resolution. In this context, we recently proposed a canonical polyadic decomposition (CPD) based algorithm for single image…

In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…

This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…

For each object in a tensor triangulated category, we construct a natural continuous map from the object's support---a closed subset of the category's triangular spectrum---to the Zariski spectrum of a certain commutative ring of…

Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…

We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…