Related papers: The trouble with tensor ring decompositions

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…

In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…

Tensor completion recovers a multi-dimensional array from a limited number of measurements. Using the recently proposed tensor ring (TR) decomposition, in this paper we show that a d-order tensor of dimensional size n and TR rank r can be…

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…

Tensor clustering has become an important topic, specifically in spatio-temporal modeling, due to its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of the day or day of the week). Our…

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention…

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…

Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some…

Point-mass filters solve Bayesian recursive relations by approximating probability density functions of a system state over grids of discrete points. The approach suffers from the curse of dimensionality. The exponential increase of the…

We propose a constructive algorithm that decomposes an arbitrary real tensor into a finite sum of orthonormal rank-1 outer products. The algorithm, named TTr1SVD, works by converting the tensor into a tensor-train rank-1 (TTr1) series via…

Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its…

Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…

Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous…

Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…

Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…

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 ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…

The subrank of tensors is a measure of how much a tensor can be ''diagonalized''. This parameter was introduced by Strassen to study fast matrix multiplication algorithms in algebraic complexity theory and is closely related to many central…

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…