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Tensor Train Factorization with Spatio-temporal Smoothness for Streaming Low-rank Tensor Completion
Estimating the missing data from an incomplete measurement or observation plays an important role in the area of big data analytic, especially for...
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Low Rank Tensor Decompositions and Approximations
There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are...
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Riemannian conjugate gradient method for low-rank tensor completion
Tensor completion aims to reconstruct a high-dimensional data from the partial element missing tensors under a low-rank constraint, which may be seen...
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Optimality conditions for Tucker low-rank tensor optimization
Optimization problems with tensor variables are widely used in statistics, machine learning, pattern recognition, signal processing, computer vision,...
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Proximal gradient algorithm for nonconvex low tubal rank tensor recovery
In this paper, we consider the three-order tensor recovery problem within the tensor tubal rank framework. Most of the recent studies under this...
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A New Tensor Multi-rank Approximation with Total Variation Regularization for Tensor Completion
In this paper, we present a novel tensor completion model which combines the Laplace function and an anisotropic total variation regularization. The...
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Rank Properties and Computational Methods for Orthogonal Tensor Decompositions
The orthogonal decomposition factorizes a tensor into a sum of an orthogonal list of rank-one tensors. The corresponding rank is called orthogonal...
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Tensor Robust Principal Component Analysis via Non-convex Low-Rank Approximation Based on the Laplace Function
Recently, the tensor robust principal component analysis (TRPCA), aiming to recover the true low-rank tensor from noisy data, has attracted...
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Enhanced Low-Rank Tensor Recovery Fusing Reweighted Tensor Correlated Total Variation Regularization for Image Denoising
Most current methods for image denoising exploit the global low-rankness and local smoothness priors of images to model them, including independent...
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Nonnegative low rank tensor approximations with multidimensional image applications
The main aim of this paper is to develop a new algorithm for computing a nonnegative low rank tensor approximation for nonnegative tensors that arise...
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Low-Rank Tensor Data Reconstruction and Denoising via ADMM: Algorithm and Convergence Analysis
Seismic data is contaminated by noise due to a variety of factors including wind, ocean currents, vehicular traffic, and construction. Further...
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Low-rank nonnegative tensor approximation via alternating projections and sketching
We show how to construct nonnegative low-rank approximations of nonnegative tensors in Tucker and tensor train formats. We use alternating...
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Low-rank tensor structure preservation in fractional operators by means of exponential sums
The use of fractional differential equations is a key tool in modeling non-local phenomena. Often, an efficient scheme for solving a linear system...
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Partially symmetric tensor structure preserving rank-R approximation via BFGS algorithm
It is known that many tensor data have symmetric or partially symmetric structure and structural tensors have structure preserving Candecomp/Parafac...
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Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based...
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Low-rank tensor methods for Markov chains with applications to tumor progression models
Cancer progression can be described by continuous-time Markov chains whose state space grows exponentially in the number of somatic mutations. The...
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On Approximation Algorithm for Orthogonal Low-Rank Tensor Approximation
This work studies solution methods for approximating a given tensor by a sum of R rank-1 tensors with one or more of the latent factors being...
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A Local Macroscopic Conservative (LoMaC) Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics
In this paper, we propose a novel Local Macroscopic Conservative (LoMaC) low rank tensor method with discontinuous Galerkin (DG) discretization for...
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The Low-Rank Approximation of Fourth-Order Partial-Symmetric and Conjugate Partial-Symmetric Tensor
We present an orthogonal matrix outer product decomposition for the fourth-order conjugate partial-symmetric (CPS) tensor and show that the greedy...
