Related papers: Tensor-based compression of the sea temperature da…
The increasing complexity of advanced materials with anisotropic thermal properties necessitates more generic and efficient methods to determine three-dimensional (3D) anisotropic thermal conductivity tensors with up to six independent…
Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…
Recovery of internet network traffic data from incomplete observed data is an important issue in internet network engineering and management. In this paper, by fully combining the temporal stability and periodicity features in internet…
Tensor classification is gaining importance across fields, yet handling partially observed data remains challenging. In this paper, we introduce a novel approach to tensor classification with incomplete data, framed within high-dimensional…
Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…
Various studies that address the compressed sensing problem with Multiple Measurement Vectors (MMVs) have been recently carried. These studies assume the vectors of the different channels to be jointly sparse. In this paper, we relax this…
The paper presents a strategy to construct an incremental Singular Value Decomposition (SVD) for time-evolving, spatially 3D discrete data sets. A low memory access procedure for reducing and deploying the snapshot data is presented.…
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for…
In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…
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…
Reliable weather forecasting is of great importance in science, business, and society. The best performing data-driven models for weather prediction tasks rely on recurrent or convolutional neural networks, where some of which incorporate…
Dynamical low-rank approximation in the Tucker tensor format of given large time-dependent tensors and of tensor differential equations is the subject of this paper. In particular, a discrete time integration method for rank-constrained…
We present a spatially efficient decomposition of matrices and arbitrary-order tensors as linear combinations of tensor products of $\{-1, 1\}$-valued vectors. For any matrix $A \in \mathbb{R}^{m \times n}$, $$A - R_w = S_w C_w T_w^\top =…
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…
This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density…
Currently, the size of scientific data is growing at an unprecedented rate. Data in the form of tensors exhibit high-order, high-dimensional, and highly sparse features. Although tensor-based analysis methods are very effective, the large…
Advanced tensor decomposition, such as Tensor train (TT) and Tensor ring (TR), has been widely studied for deep neural network (DNN) model compression, especially for recurrent neural networks (RNNs). However, compressing convolutional…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional function approximations arising from computational and data sciences. Various sequential and parallel TT decomposition algorithms have…
Despite the recent success of deep learning models in numerous applications, their widespread use on mobile devices is seriously impeded by storage and computational requirements. In this paper, we propose a novel network compression method…