Related papers: The tensor hypercontracted parametric reduced dens…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

This paper proposes an low power approximate multiplier architecture for deep neural network (DNN) applications. A 4:2 compressor, introducing only a single combination error, is designed and integrated into an 8x8 unsigned multiplier. This…

In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors. Tensor contraction is a popular operation on tensors to exploit meaning or alter…

This paper presents low-complexity tensor completion algorithms and their efficient implementation to reconstruct highly oscillatory operators discretized as $n\times n$ matrices. The underlying tensor decomposition is based on the…

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…

Nearest-neighbor search in large vector databases is crucial for various machine learning applications. This paper introduces a novel method using tensor-train (TT) low-rank tensor decomposition to efficiently represent point clouds and…

The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field, the geometric inner-product structure suffices to introduce…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

In order to achieve high efficiency of classification in intrusion detection, a compressed model is proposed in this paper which combines horizontal compression with vertical compression. OneR is utilized as horizontal com-pression for…

The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral…

The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…

Tensor clustering has become an important topic, specifically in spatio-temporal modeling, due to its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of the day or day of the week). Our…

The problem of partitioning a large and sparse tensor is considered, where the tensor consists of a sequence of adjacency matrices. Theory is developed that is a generalization of spectral graph partitioning. A best rank-$(2,2,\lambda)$…

Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be…

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…

Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…