Related papers: A Randomized Algorithm for Tensor Singular Value D…

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and…

We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…

The generalized singular value decomposition (GSVD) is a powerful tool for solving discrete ill-posed problems. In this paper, we propose a two-sided uniformly randomized GSVD algorithm for solving the large-scale discrete ill-posed problem…

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

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…

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,…

In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous time levels leads to storage requirements that grow…

Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…

Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…

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…

Tensor computation has emerged as a powerful mathematical tool for solving high-dimensional and/or extreme-scale problems in science and engineering. The last decade has witnessed tremendous advancement of tensor computation and its…

Singular value decomposition is widely used in modal analysis, such as proper orthogonal decomposition and resolvent analysis, to extract key features from complex problems. SVD derivatives need to be computed efficiently to enable the…

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained…

Recently, numerous tensor singular value decomposition (t-SVD)-based tensor recovery methods have shown promise in processing visual data, such as color images and videos. However, these methods often suffer from severe performance…

From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have…

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…

The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…

We present a variational quantum circuit that produces the Singular Value Decomposition of a bipartite pure state. The proposed circuit, that we name Quantum Singular Value Decomposer or QSVD, is made of two unitaries respectively acting on…

The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…