Results 11 to 20 of about 10,455 (264)
Provable tensor ring completion [PDF]
Signal Processing, 2020 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 exactly recovered with high probability by solving a convex optimization program, given n^{d/2} r^2 ln^7(n^{d/2 ...
Huyan Huang +3 more
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Completely Positive Binary Tensors [PDF]
Mathematics of Operations Research, 2019 A symmetric tensor is completely positive (CP) if it is a sum of tensor powers of nonnegative vectors. This paper characterizes completely positive binary tensors. We show that a binary tensor is completely positive if and only if it satisfies two linear matrix inequalities.
Jinyan Fan, Jiawang Nie, Anwa Zhou
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Spectral Algorithms for Tensor Completion [PDF]
Communications on Pure and Applied Mathematics, 2018 In the tensor completion problem, one seeks to estimate a low‐rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational resources (using, for instance, tensor nuclear norm minimization) and polynomial‐time algorithms. Among the latter,
Andrea Montanari, Nike Sun
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Tensor Completion in Hierarchical Tensor Representations [PDF]
, 2015 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 reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number ...
Holger Rauhut +2 more
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Dehomogenization for completely positive tensors
Numerical Algebra, Control and Optimization, 2023 25 ...
Nie, Jiawang +3 more
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Deterministic Tensor Completion with Hypergraph Expanders
SIAM Journal on Mathematics of Data Science, 2021 We provide a novel analysis of low-rank tensor completion based on hypergraph expanders. As a proxy for rank, we minimize the max-quasinorm of the tensor, which generalizes the max-norm for matrices. Our analysis is deterministic and shows that the number of samples required to approximately recover an order-$t$ tensor with at most $n$ entries per ...
Kameron Decker Harris, Yizhe Zhu
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Robust Tensor Factorization for Color Image and Grayscale Video Recovery
IEEE Access, 2020 Low-rank tensor completion (LRTC) plays an important role in many fields, such as machine learning, computer vision, image processing, and mathematical theory.
Shiqiang Du +4 more
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Latent Matrices for Tensor Network Decomposition and to Tensor Completion
CoRR, 2022 The prevalent fully-connected tensor network (FCTN) has achieved excellent success to compress data. However, the FCTN decomposition suffers from slow computational speed when facing higher-order and large-scale data. Naturally, there arises an interesting question: can a new model be proposed that decomposes the tensor into smaller ones and speeds up ...
Peilin Yang +3 more
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Missing Data Recovery Based on Tensor-CUR Decomposition
IEEE Access, 2018 Tensor completion is a higher way analog of matrix completion, which has proven to be a powerful tool for data analysis. In this paper, we formulate the missing data recovery problem of a three-way tensor as a tensor completion problem.
Lele Wang +3 more
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Hierarchical Tensor Ring Completion
CoRR, 2020 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, existing algorithms need predefined tensor ring rank which may be hard to determine in practice.
Abdul Ahad +3 more
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