Related papers: A higher-order singular value decomposition tensor…
Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix…
This is an introductory survey, from a geometric perspective, on the Singular Value Decomposition (SVD) for real matrices, focusing on the role of the Terracini Lemma. We extend this point of view to tensors, we define the singular space of…
In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg--Landau equations on Cartesian product domains with homogeneous Dirichlet/Neumann or periodic boundary conditions. To this…
In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (R3SVD) algorithm is used to adaptively carry out partial…
Multi-output Gaussian process regression has become an important tool in uncertainty quantification, for building emulators of computationally expensive simulators, and other areas such as multi-task machine learning. We present a holistic…
In this paper, we mainly develop the well-known vector and matrix polynomial extrapolation methods in tensor framework. To this end, some new products between tensors are defined and the concept of positive definitiveness is extended for…
Modeling the dynamic behavior of deformable objects is crucial for creating realistic digital worlds. While conventional simulations produce high-quality motions, their computational costs are often prohibitive. Subspace simulation…
Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…
The Tucker decomposition generalizes the notion of Singular Value Decomposition (SVD) to tensors, the higher dimensional analogues of matrices. We study the problem of constructing the Tucker decomposition of sparse tensors on distributed…
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…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…
In this work, a new algorithm based on the application of higher-order dynamic mode decomposition (HODMD) is proposed for feature selection and variables clustering in reacting flow simulations. The hierarchical HODMD (h-HODMD) performs a…
A promising area of applications for quantum computing is in linear algebra problems. In this work, we introduce two new quantum t-SVD (tensor-SVD) algorithms. The first algorithm is largely based on previous work that proposed a quantum…
We derive methods to compute higher order differentials (Hessians and Hessian-vector products) of the rendering operator. Our approach is based on importance sampling of a convolution that represents the differentials of rendering…
Matrix factorizations in dual number algebra, a hypercomplex system, have been applied to kinematics, mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves…
One of the possible objectives when designing experiments is to build or formulate a model for predicting future observations. When the primary objective is prediction, some typical approaches in the planning phase are to use…
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
First-order stochastic methods for solving large-scale non-convex optimization problems are widely used in many big-data applications, e.g. training deep neural networks as well as other complex and potentially non-convex machine learning…
Value decomposition (VD) has become one of the most prominent solutions in cooperative multi-agent reinforcement learning. Most existing methods generally explore how to factorize the joint value and minimize the discrepancies between agent…
Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed can enable new studies of fundamental science as well as more potential applications. In this work we discuss solving a system of…