相关论文: Low-Multi-Rank High-Order Bayesian Robust Tensor F…

The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…

Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…

Tensor-based multi-view subspace clustering (MSC) can capture high-order correlation in the self-representation tensor. Current tensor decompositions for MSC suffer from highly unbalanced unfolding matrices or rotation sensitivity, failing…

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

This paper introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular modes. The problem is motivated by high-order longitudinal data…

Motivated by the challenges of analyzing high-dimensional ($p \gg n$) sequencing data from longitudinal microbiome studies, where samples are collected at multiple time points from each subject, we propose supervised functional tensor…

Low rank tensor representation (LRTR) methods are very useful for hyperspectral anomaly detection (HAD). To overcome the limitations that they often overlook spectral anomaly and rely on large-scale matrix singular value decomposition, we…

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

Dimensionality reduction methods, such as principal component analysis (PCA) and factor analysis, are central to many problems in data science. There are, however, serious and well-understood challenges to finding robust low dimensional…

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…

Multitask learning (MTL) leverages task-relatedness to enhance performance. With the emergence of multimodal data, tasks can now be referenced by multiple indices. In this paper, we employ high-order tensors, with each mode corresponding to…

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…

A new submodule clustering method via sparse and low-rank representation for multi-way data is proposed in this paper. Instead of reshaping multi-way data into vectors, this method maintains their natural orders to preserve data intrinsic…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

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…

Tensor numerical methods, based on the rank-structured tensor representation of $d$-variate functions and operators, are designed to provide $O(dn)$ complexity of numerical calculations on $n^{\otimes d }$ grids contrary to $O(n^d)$ scaling…

The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…