Related papers: Effective Tensor Sketching via Sparsification

In this paper, we investigate the sample size requirement for a general class of nuclear norm minimization methods for higher order tensor completion. We introduce a class of tensor norms by allowing for different levels of coherence, which…

This work discusses tensor network embeddings, which are random matrices ($S$) with tensor network structure. These embeddings have been used to perform dimensionality reduction of tensor network structured inputs $x$ and accelerate…

Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…

Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…

High-dimensional sparse data present computational and statistical challenges for supervised learning. We propose compact linear sketches for reducing the dimensionality of the input, followed by a single layer neural network. We show that…

Low-tubal-rank tensor approximation has been proposed to analyze large-scale and multi-dimensional data. However, finding such an accurate approximation is challenging in the streaming setting, due to the limited computational resources. To…

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-$(2,2,\lambda)$…

Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression…

Based on sketching techniques, we propose two randomized algorithms for tensor ring (TR) decomposition. Specifically, by defining new tensor products and investigating their properties, we apply the Kronecker sub-sampled randomized Fourier…

In this work, we develop deterministic and random sketching-based algorithms for two types of tensor interpolative decompositions (ID): the core interpolative decomposition (CoreID, also known as the structure-preserving HOSVD) and the…

A seminal work of [Ahn-Guha-McGregor, PODS'12] showed that one can compute a cut sparsifier of an unweighted undirected graph by taking a near-linear number of linear measurements on the graph. Subsequent works also studied computing other…

We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

High-order clustering aims to classify objects in multiway datasets that are prevalent in various fields such as bioinformatics, recommendation systems, and social network analysis. Such data are often sparse and high-dimensional, posing…

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Sparse tensor operations are increasingly important in diverse applications such as social networks, deep learning, diagnosis, crime, and review analysis. However, a major obstacle in sparse tensor research is the lack of large-scale sparse…

Sparse tensors are prevalent in many data-intensive applications, yet existing differentiable programming frameworks are tailored towards dense tensors. This presents a significant challenge for efficiently computing gradients through…

In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…