Related papers: Efficient Alternating Least Squares Algorithms for…

In this paper, we propose a new adaptive cross algorithm for computing a low tubal rank approximation of third-order tensors, with less memory and lower computational complexity than the truncated tensor SVD (t-SVD). This makes it…

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…

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points…

Tensor decompositions, such as CANDECOMP/PARAFAC (CP), are widely used in a variety of applications, such as chemometrics, signal processing, and machine learning. A broadly used method for computing such decompositions relies on the…

The alternating least squares (ALS/AltLS) method is a widely used algorithm for computing the CP decomposition of a tensor. However, its convergence theory is still incompletely understood. In this paper, we prove explicit quantitative…

We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating…

Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…

This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…

Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the…

Matrix factorization is an important representation learning algorithm, e.g., recommender systems, where a large matrix can be factorized into the product of two low dimensional matrices termed as latent representations. This paper…

Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace…

This article focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas…

This paper presents a novel adaptive reduced-rank {multi-input multi-output} (MIMO) equalization scheme and algorithms based on alternating optimization design techniques for MIMO spatial multiplexing systems. The proposed reduced-rank…

In this paper we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least-squares (ALS). Since the function has size exponential in $d$ where $d$ is the number of dimensions,…

In this paper, we discuss the acceleration of the regularized alternating least square (RALS) algorithm for tensor approximation. We propose a fast iterative method using a Aitken-Stefensen like updates for the regularized algorithm.…

This paper presents novel adaptive space-time reduced-rank interference suppression least squares algorithms based on joint iterative optimization of parameter vectors. The proposed space-time reduced-rank scheme consists of a joint…

Low rank tensor completion is a highly ill-posed inverse problem, particularly when the data model is not accurate, and some sort of regularization is required in order to solve it. In this article we focus on the calibration of the data…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…