• Publications
  • Influence
Tensor Decompositions and Applications
This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order
Efficient MATLAB Computations with Sparse and Factored Tensors
TLDR
This paper considers how specially structured tensors allow for efficient storage and computation, and proposes storing sparse tensors using coordinate format and describes the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms.
All-at-once Optimization for Coupled Matrix and Tensor Factorizations
TLDR
An all-at-once optimization approach for coupled matrix and tensor factorization (CMTF) problem where heterogeneous data sets are modeled by fitting outer-product models to higher-order tensors and matrices in a coupled manner is proposed.
Multilinear operators for higher-order decompositions
  • T. Kolda
  • Mathematics, Computer Science
  • 1 April 2006
TLDR
Two new multilinear operators are proposed for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions and one of them is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor.
Algorithm 862: MATLAB tensor classes for fast algorithm prototyping
TLDR
Four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping are described and their use is demonstrated by showing how to implement several tensor algorithms that have appeared in the literature.
On Tensors, Sparsity, and Nonnegative Factorizations
TLDR
This paper proposes that the random variation is best described via a Poisson distribution, which better describes the zeros observed in the data as compared to the typical assumption of a Gaussian distribution, and presents a new algorithm for Poisson tensor factorization called CANDECOMP--PARAFAC alternating Poisson regression (CP-APR), based on a majorization-minimization approach.
Shifted Power Method for Computing Tensor Eigenpairs
TLDR
A shifted symmetric higher-order power method (SS-HOPM), which it is shown is guaranteed to converge to a tensor eigenpair, and a fixed point analysis is used to characterize exactly which eigenpairs can and cannot be found by the method.
DAKOTA , A Multilevel Parallel Object-Oriented Framework for Design Optimization , Parameter Estimation , Uncertainty Quantification , and Sensitivity Analysis Version 4 . 0 User ’ s Manual
TLDR
This report serves as a user’s manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.
Community structure and scale-free collections of Erdös-Rényi graphs
TLDR
The Block Two-Level Erdős-Rényi (BTER) model is proposed, and it is demonstrated that it accurately captures the observable properties of many real-world social networks.
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