Related papers: Einstien-Multidimensional Extrapolation methods
We describe a new method called t-ETE for finding a low-dimensional embedding of a set of objects in Euclidean space. We formulate the embedding problem as a joint ranking problem over a set of triplets, where each triplet captures the…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately…
We introduce the definition of tensorized block rational Krylov subspaces and its relation with multivariate rational functions, extending the formulation of tensorized Krylov subspaces introduced in [Kressner D., Tobler C., Krylov subspace…
We present new techniques for reducing a multivariate sparse polynomial to a univariate polynomial. The reduction works similarly to the classical and widely-used Kronecker substitution, except that we choose the degrees randomly based on…
We investigate the acceleration of stationary iterations for multi-term Sylvester equation by means of reduced rank extrapolation (RRE). Theoretical convergence results and implementations are provided for both small and large-scale…
Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on…
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies…
Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…
Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimension of very high-dimensional tensors. Following the work in [30], we consider a tensorized random…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
A new submodule clustering method via sparse and low-rank representation for multi-way data is proposed in this paper. Instead of reshaping multi-way data into vectors, this method maintains their natural orders to preserve data intrinsic…
We consider the problem of interpolating a sparse multivariate polynomial over a finite field, represented with a black box. Building on the algorithm of Ben-Or and Tiwari for interpolating polynomials over rings with characteristic zero,…
Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…
In this paper, we propose different algorithms for the solution of a tensor linear discrete ill-posed problem arising in the application of the meshless method for solving PDEs in three-dimensional space using multiquadric radial basis…
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…
In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/ significant lateral and horizontal slices/features. The proposed Tubal DEIM…
Global discrete optimization is notoriously difficult due to the lack of gradient information and the curse of dimensionality, making exhaustive search infeasible. Tensor cross approximation is an efficient technique to approximate…