相关论文: Robust Low-rank Tensor Train Recovery

Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…

The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT)…

Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem…

We introduce the tubal tensor train (TTT) decomposition, a tensor-network model that combines the t-product algebra of the tensor singular value decomposition (T-SVD) with the low-order core structure of the tensor train (TT) format. For an…

Radio Frequency Neural Networks (RFNNs) have demonstrated advantages in realizing intelligent applications across various domains. However, as the model size of deep neural networks rapidly increases, implementing large-scale RFNN in…

In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…

The essential task of tensor data analysis focuses on the tensor decomposition and the corresponding notion of rank. In this paper, by introducing the notion of tensor Singular Value Decomposition (t-SVD), we establish a Regularized Tensor…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

Tensor Train~(TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate…

In this article, we derive a semi-Lagrangian scheme for the solution of the Vlasov equation represented as a low-parametric tensor. Grid-based methods for the Vlasov equation have been shown to give accurate results but their use has mostly…

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated…

In this paper, we study a Bayesian tensor train (TT) decomposition method to recover streaming data by approximating the latent structure in high-order streaming data. Drawing on the streaming variational Bayes method, we introduce the TT…

Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th…

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…

We propose an efficient implementation of the numerical tensor-train (TT) based algorithm solving the multicomponent coagulation equation preserving the nonnegativeness of solution. Unnatural negative elements in the constructed…