相关论文: Truncated nuclear norm regularization for low-rank…

Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have…

Atomic norm minimization is a convex optimization framework to recover point sources from a subset of their low-pass observations, or equivalently the underlying frequencies of a spectrally-sparse signal. When the amplitudes of the sources…

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

Recurrent Neural Network (RNN) are a popular choice for modeling temporal and sequential tasks and achieve many state-of-the-art performance on various complex problems. However, most of the state-of-the-art RNNs have millions of parameters…

We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

Noise is ubiquitous during image acquisition. Sufficient denoising is often an important first step for image processing. In recent decades, deep neural networks (DNNs) have been widely used for image denoising. Most DNN-based image…

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization…

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…

The prevalence of data collected on the same set of samples from multiple sources (i.e., multi-view data) has prompted significant development of data integration methods based on low-rank matrix factorizations. These methods decompose…

We propose a block coordinate descent type algorithm for estimating the rank of a given tensor. In addition, the algorithm provides the canonical polyadic decomposition of a tensor. In order to estimate the tensor rank we use sparse…

This paper describes and compares some structure preserving techniques for the solution of linear discrete ill-posed problems with the t-product. A new randomized tensor singular value decomposition (R-tSVD) with a t-product is presented…

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…

In color image processing, image completion aims to restore missing entries from the incomplete observation image. Recently, great progress has been made in achieving completion by approximately solving the rank minimization problem. In…

We propose a new tensor network renormalization group (TNR) scheme based on global optimization and introduce a new method for constructing the finite-temperature density matrix of two-dimensional quantum systems. Combining these two into a…

The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies…

Tensor completion is a core machine learning algorithm used in recommender systems and other domains with missing data. While the matrix case is well-understood, theoretical results for tensor problems are limited, particularly when the…

In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…