Related papers: Tensor Completion Made Practical
In this work, a tensor completion problem is studied, which aims to perfectly recover the tensor from partial observations. The existing theoretical guarantee requires the involved transform to be orthogonal, which hinders its applications.…
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…
To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic…
In this paper, we propose a novel tensor learning and coding model for third-order data completion. Our model is to learn a data-adaptive dictionary from the given observations, and determine the coding coefficients of third-order 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)…
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,…
Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor…
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…
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…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…
Tensor completion is a core machine learning algorithm used in recommender systems and other domains with missing data. While the matrix case is well-understood, theoretical results for tensor problems are limited, particularly when the…
In recent studies, the tensor ring (TR) rank has shown high effectiveness in tensor completion due to its ability of capturing the intrinsic structure within high-order tensors. A recently proposed TR rank minimization method is based on…
Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…
We consider a novel algorithm, for the completion of partially observed low-rank tensors, where each entry of the tensor can be chosen from a discrete finite alphabet set, such as in common image processing problems, where the entries…
We introduce a new consistency-based approach for defining and solving nonnegative/positive matrix and tensor completion problems. The novelty of the framework is that instead of artificially making the problem well-posed in the form of an…
The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…