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We show a way to perform the canonical renormalization group (RG) prescription in tensor space: write down the tensor RG equation, linearize it around a fixed-point tensor, and diagonalize the resulting linearized RG equation to obtain…
In real-world scenarios, complex data such as multispectral images and multi-frame videos inherently exhibit robust low-rank property. This property is vital for multi-dimensional inverse problems, such as tensor completion, spectral…
Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled…
The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…
Randomized methods, such as the randomized SVD (singular value decomposition) and Nystr\"om approximation, are an effective way to compute low-rank approximations of large matrices. Motivated by applications to operator learning, Boull\'e…
Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens…
In this work, we propose a new discretization for second-order total generalized variation (TGV) with some distinct properties compared to existing discrete formulations. The introduced model is based on same design principles as Condat's…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
We introduce the tubal tensor train (TTT) decomposition, a tensor-network model that combines the t-product algebra of the tensor singular value decomposition (T-SVD) with the low-order core structure of the tensor train (TT) format. For an…
The singular value decomposition (SVD) and the principal component analysis are fundamental tools and probably the most popular methods for data dimension reduction. The rapid growth in the size of data matrices has lead to a need for…
Higher-order singular value decomposition (HOSVD) is an efficient way for data reduction and also eliciting intrinsic structure of multi-dimensional array data. It has been used in many applications, and some of them involve incomplete…
The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and strong theoretical guarantees. Recent work by Boull\'e and…
There are several factorizations of multi-dimensional tensors into lower-dimensional components, known as `tensor networks'. We consider the popular `tensor-train' (TT) format and ask: How efficiently can we compute a low-rank approximation…
Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank…
We present a simple yet novel parameterized form of linear mapping to achieves remarkable network compression performance: a pseudo SVD called Ternary SVD (TSVD). Unlike vanilla SVD, TSVD limits the $U$ and $V$ matrices in SVD to ternary…
We introduce methodology to construct an emulator for environmental and ecological spatio-temporal processes that uses the higher order singular value decomposition (HOSVD) as an extension of singular value decomposition (SVD) approaches to…
A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for $L_1$-norm…
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 study the logarithmic correction to the scaling of the first Lee-Yang (LY) zero in the classical $XY$ model on square lattices by using tensor renormalization group methods. In comparing the higher-order tensor renormalization group…
Color images and video sequences can be modeled as three-way tensors, which admit low tubal-rank approximations via convex surrogate minimization. This optimization problem is efficiently addressed by tensor singular value thresholding…