Related papers: Accelerated Tensor Completion via Trace-Regularize…

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…

Remote sensing image (RSI) inpainting plays an important role in real applications. Recently, fully-connected tensor network (FCTN) decomposition has been shown the remarkable ability to fully characterize the global correlation.…

Recently, tensor fibered rank has demonstrated impressive performance by effectively leveraging the global low-rank property in all directions for low-rank tensor completion (LRTC). However, it still has some limitations. Firstly, the…

We consider a novel algorithm, for the completion of partially observed low-rank tensors, as a generalization of matrix completion. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN)…

Existing tensor completion formulation mostly relies on partial observations from a single tensor. However, tensors extracted from real-world data are often more complex due to: (i) Partial observation: Only a small subset (e.g., 5%) of…

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…

We propose and evaluate new techniques for compressing and speeding up dense matrix multiplications as found in the fully connected and recurrent layers of neural networks for embedded large vocabulary continuous speech recognition (LVCSR).…

Dimension reduction techniques are often used when the high-dimensional tensor has relatively low intrinsic rank compared to the ambient dimension of the tensor. The CANDECOMP/PARAFAC (CP) tensor completion is a widely used approach to find…

The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn…

In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…

Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…

We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the…

Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…

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…

Tensor ring (TR) decomposition is an efficient approach to discover the hidden low-rank patterns for higher-order tensors, and streaming tensors are becoming highly prevalent in real-world applications. In this paper, we investigate how to…

Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in…

In this paper we propose an algorithm to classify tensor data. Our methodology is built on recent studies about matrix classification with the trace norm constrained weight matrix and the tensor trace norm. Similar to matrix classification,…

Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observation with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the…

Tensor completion recovers a multi-dimensional array from a limited number of measurements. Using the recently proposed tensor ring (TR) decomposition, in this paper we show that a d-order tensor of dimensional size n and TR rank r can be…

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…