Related papers: Scalable Tucker Factorization for Sparse Tensors -…

We propose an isogeometric solver for Poisson problems that combines i)low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, ii) a Truncated…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…

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…

We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…

Missing value problem in spatiotemporal traffic data has long been a challenging topic, in particular for large-scale and high-dimensional data with complex missing mechanisms and diverse degrees of missingness. Recent studies based on…

Topic models have become popular tools for dimension reduction and exploratory analysis of text data which consists in observed frequencies of a vocabulary of $p$ words in $n$ documents, stored in a $p\times n$ matrix. The main premise is…

Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…

Sparse Tensor Compilers (STCs) have emerged as critical infrastructure for optimizing high-dimensional data analytics and machine learning workloads. The STCs must synthesize complex, irregular control flow for various compressed storage…

There is an emerging interest in tensor factorization applications in big-data analytics and machine learning. To speed up the factorization of extra-large datasets, organized in multidimensional arrays (aka tensors), easy to compute…

Given a high-dimensional large-scale tensor, how can we decompose it into latent factors? Can we process it on commodity computers with limited memory? These questions are closely related to recommender systems, which have modeled rating…

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

Data tensors of orders 2 and greater are now routinely being generated. These data collections are increasingly huge and growing. Many scientific and medical data tensors are tensor fields (e.g., images, videos, geographic data) in which…

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…

We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…

Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are…

Scalable sparse LU factorization is critical for efficient numerical simulation of circuits and electrical power grids. In this work, we present a new scalable sparse direct solver called Basker. Basker introduces a new algorithm to…

In this paper, we study the problem of a batch of linearly correlated image alignment, where the observed images are deformed by some unknown domain transformations, and corrupted by additive Gaussian noise and sparse noise simultaneously.…