Related papers: Low-CP-rank Tensor Completion via Practical Regula…

Low-rank tensor completion (LRTC) is an important problem in computer vision and machine learning. The minimax-concave penalty (MCP) function as a non-convex relaxation has achieved good results in the LRTC problem. To makes all the…

The PARAFAC2 model provides a flexible alternative to the popular CANDECOMP/PARAFAC (CP) model for tensor decompositions. Unlike CP, PARAFAC2 allows factor matrices in one mode (i.e., evolving mode) to change across tensor slices, which has…

Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization…

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 CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We…

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…

Canonical Polyadic (or CANDECOMP/PARAFAC, CP) decompositions (CPD) are widely applied to analyze high order tensors. Existing CPD methods use alternating least square (ALS) iterations and hence need to unfold tensors to each of the $N$…

We propose an adaptive and provably accurate tensor completion approach based on combining matrix completion techniques (see, e.g., arXiv:0805.4471, arXiv:1407.3619, arXiv:1306.2979) for a small number of slices with a modified noise robust…

Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…

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)…

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…

Tensor decompositions have proven to be effective in analyzing the structure of multidimensional data. However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP/PARAFAC…

The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…

Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…

We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the…

Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…

The problem of Knowledge Base Completion can be framed as a 3rd-order binary tensor completion problem. In this light, the Canonical Tensor Decomposition (CP) (Hitchcock, 1927) seems like a natural solution; however, current implementations…

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…