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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…

Matrices can be decomposed via rank-one approximations: the best rank-one approximation is a singular vector pair, and the singular value decomposition writes a matrix as a sum of singular vector pairs. The singular vector tuples of a…

We present two new algorithms for approximating and updating the hierarchical Tucker decomposition of tensor streams. The first algorithm, Batch Hierarchical Tucker - leaf to root (BHT-l2r), proposes an alternative and more efficient way of…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

Large language models have become ubiquitous in modern life, finding applications in various domains such as natural language processing, language translation, and speech recognition. Recently, a breakthrough work [Zhao, Panigrahi, Ge, and…

Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…

Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…

Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

In this paper we study the problem of decomposing a given tensor into a tensor train such that the tensors at the vertices are orthogonally decomposable. When the tensor train has length two, and the orthogonally decomposable tensors at the…

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…

In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…

The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…

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…

We present a new approximation algorithm for the treewidth problem which finds an upper bound on the treewidth and constructs a corresponding tree decomposition as well. Our algorithm is a faster variation of Reed's classical algorithm. For…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn…

We consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in…

The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states…

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…