Related papers: Multilinear Low-Rank Tensors on Graphs & Applicati…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver…

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…

There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank…

The overfitting is one of the cursing subjects in the deep learning field. To solve this challenge, many approaches were proposed to regularize the learning models. They add some hyper-parameters to the model to extend the generalization;…

Learning neural fields has been an active topic in deep learning research, focusing, among other issues, on finding more compact and easy-to-fit representations. In this paper, we introduce a novel low-rank representation termed Tensor…

We study low-rank parameterizations of weight matrices with embedded spectral properties in the Deep Learning context. The low-rank property leads to parameter efficiency and permits taking computational shortcuts when computing mappings.…

This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…

A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…

This work presents a low-rank tensor model for multi-dimensional Markov chains. A common approach to simplify the dynamical behavior of a Markov chain is to impose low-rankness on the transition probability matrix. Inspired by the success…

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…

Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…

Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The…

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…

Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank optimization problems to be challenging. To this end, we…