Related papers: Robust Tensor Completion via Gradient Tensor Nulcl…

Graph representation learning, involving both node features and graph structures, is crucial for real-world applications but often encounters pervasive noise. State-of-the-art methods typically address noise by focusing separately on node…

The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…

For subspace recovery, most existing low-rank representation (LRR) models performs in the original space in single-layer mode. As such, the deep hierarchical information cannot be learned, which may result in inaccurate recoveries for…

Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since robust loss…

In recent years, graph neural networks (GNN) have achieved significant developments in a variety of graph analytical tasks. Nevertheless, GNN's superior performance will suffer from serious damage when the collected node features or…

Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

In this paper, we study the problem of robust subspace recovery (RSR) in the presence of both strong adversarial corruptions and Gaussian noise. Specifically, given a limited number of noisy samples -- some of which are tampered by an…

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently…

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…

Noise robust compressive sensing algorithm is considered. This algorithm allows an efficient signal reconstruction in the presence of different types of noise due to the possibility to change minimization norm. For instance, the commonly…

Low-rank tensor representation (LRTR) has emerged as a powerful tool for multi-dimensional data processing. However, classical LRTR-based methods face two critical limitations: (1) they typically assume that the holistic data is low-rank,…

In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and low rank matrix completion (MC) is studied. The problem is formulated as a nonconvex regularized leat square optimization problems, in which the l0-norm and the…

To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph…

Tucker decomposition is a common method for the analysis of multi-way/tensor data. Standard Tucker has been shown to be sensitive against heavy corruptions, due to its L2-norm-based formulation which places squared emphasis to peripheral…

Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of low-rank tensor factorization (LRTF) has been applied for the recovery of a low dimensional subspace from high dimensional…

The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…

Despite the prevalence of retrieval-augmented language models (RALMs), the seamless integration of these models with retrieval mechanisms to enhance performance in document-based tasks remains challenging. While some post-retrieval…

In order to compute the best low-rank tensor approximation using the Multilinear Tensor Decomposition (MTD) model, it is essential to estimate the rank of the underlying multilinear tensor from the noisy observation tensor. In this paper,…

Many applications in data analysis rely on the decomposition of a data matrix into a low-rank and a sparse component. Existing methods that tackle this task use the nuclear norm and L1-cost functions as convex relaxations of the rank…