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Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The widely used alternating least squares (ALS) method, which solves a sequence of over-determined least squares subproblems, is costly for large and sparse…
Given a large tensor, how can we decompose it to sparse core tensor and factor matrices such that it is easier to interpret the results? How can we do this without reducing the accuracy? Existing approaches either output dense results or…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the…
Distributed sparse block codes (SBCs) exhibit compact representations for encoding and manipulating symbolic data structures using fixed-width vectors. One major challenge however is to disentangle, or factorize, the distributed…
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…
As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…
In probabilistic principal component analysis (PPCA), an observed vector is modeled as a linear transformation of a low-dimensional Gaussian factor plus isotropic noise. We generalize PPCA to tensors by constraining the loading operator to…
The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision,…
Whether for fundamental studies or nuclear data evaluations, first-principle calculations of atomic nuclei constitute the path forward. Today, performing \textit{ab initio} calculations (a) of heavy nuclei, (b) of doubly open-shell nuclei…
Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap…
Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has a symmetric nonnegative factorization, is called a…
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 time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA),…
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…
Predicting tensorial properties with machine learning models typically requires carefully designed tensorial descriptors. In this work, we introduce an alternative strategy for learning tensorial quantities based on scalar descriptors. We…
Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of…
Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights…
The PC algorithm is a widely used method in causal inference for learning the structure of Bayesian networks. Despite its popularity, the PC algorithm suffers from significant time complexity, particularly as the size of the dataset…