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Missing entries in multi dimensional data pose significant challenges for downstream analysis across diverse real world applications. These data are naturally represented as tensors, and recent completion methods integrating global low rank…

Tensor linear regression is an important and useful tool for analyzing tensor data. To deal with high dimensionality, CANDECOMP/PARAFAC (CP) low-rank constraints are often imposed on the coefficient tensor parameter in the (penalized)…

A new paradigm for large-scale spectrum occupancy learning based on long short-term memory (LSTM) recurrent neural networks is proposed. Studies have shown that spectrum usage is a highly correlated time series. Moreover, there is a…

A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor…

In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…

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)…

The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can…

In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding scheme. To overcome this drawback, a…

This paper presents a new framework of identifying a series of cyber data attacks on power system synchrophasor measurements. We focus on detecting "unobservable" cyber data attacks that cannot be detected by any existing method that purely…

The impedances of cables and lines used in (multi-conductor) distribution networks are usually unknown or approximated, and may lead to problematic results for any physics-based power system calculation, e.g., (optimal) power flow. Learning…

Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…

We introduce the dynamics mode decomposition for monitoring wide-area power grid networks from sparse measurement data. The mathematical framework fuses data from multiple sensors based on multivariate statistics, providing accurate full…

Tensor completion is a technique of filling missing elements of the incomplete data tensors. It being actively studied based on the convex optimization scheme such as nuclear-norm minimization. When given data tensors include some noises,…

Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete…

The Candecomp/Parafac (CP) decomposition of the tensor whose maximal dimension is greater than its rank is considered. We derive the upper bound of rank under which the generic uniqueness of CP decomposition is guaranteed. The bound only…

Deep Neural Networks (DNNs) have already become a crucial computational approach to revealing the spatial patterns in the human brain; however, there are three major shortcomings in utilizing DNNs to detect the spatial patterns in…

Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically…

Low voltage distribution networks (LVDNs) suffer from limited visibility due to sparse or nonexistent measurement systems, leaving distribution network service providers with incomplete data. Maintenance activities, such as transformer…

Power system cyber-physical uncertainties, including measurement ambiguities stemming from cyber attacks and data losses, along with system uncertainties introduced by massive renewables and complex dynamics, reduce the likelihood of…

In this paper we develop two new Tensor Alternating Steepest Descent algorithms for tensor completion in the low-rank $\star_{M}$-product format, whereby we aim to reconstruct an entire low-rank tensor from a small number of measurements…