640 citations · 3.8k across the 44 of their papers we have counts for
21 papers · 1 filter
The Fascinating World of 2 2 2 Tensors: Its Geometry and Optimization Challenges
Gabriel H. Brown, Joe Kileel, Tamara G. Kolda
This educational article highlights the geometric and algebraic complexities that distinguish tensors from matrices, to supplement coverage in advanced courses on linear algebra, m…
Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data
Brett W. Larsen, Tamara G. Kolda, Anru R. Zhang +1
The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some o…
Scalable symmetric Tucker tensor decomposition
Ruhui Jin, Joe Kileel, Tamara G. Kolda +1
We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special struc…
Revisiting Approximate Leverage Score Sketching for Matrix Least Squares
Brett W. Larsen, Tamara G. Kolda
We revisit the problem of sketching using approximate leverage scores for matrix least squares problems of the form where the design matrix $A \in \mathbb{R}^{N…
Streaming Generalized Canonical Polyadic Tensor Decompositions
Eric Phipps, Nick Johnson, Tamara G. Kolda
In this paper, we develop a method which we call OnlineGCP for computing the Generalized Canonical Polyadic (GCP) tensor decomposition of streaming data. GCP differs from tradition…
Estimating Higher-Order Moments Using Symmetric Tensor Decomposition
Samantha Sherman, Tamara G. Kolda
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 mean…
Stochastic Gradients for Large-Scale Tensor Decomposition
Tamara G. Kolda, David Hong
Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomp…
Generalized Canonical Polyadic Tensor Decomposition
David Hong, Tamara G. Kolda, Jed A. Duersch
Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work devel…
A Practical Randomized CP Tensor Decomposition
Casey Battaglino, Grey Ballard, Tamara G. Kolda
The CANDECOMP/PARAFAC (CP) decomposition is a leading method for the analysis of multiway data. The standard alternating least squares algorithm for the CP decomposition (CP-ALS) i…
Parallel Tensor Compression for Large-Scale Scientific Data
Woody Austin, Grey Ballard, Tamara G. Kolda
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-dim…
Symmetric Orthogonal Tensor Decomposition is Trivial
Tamara G. Kolda
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued, pairwise orthogonal vectors. Such decompositions do not generally…
Numerical Optimization for Symmetric Tensor Decomposition
Tamara G. Kolda
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued deco…
An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs
Tamara G. Kolda, Jackson R. Mayo
Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson…
Newton-Based Optimization for Kullback-Leibler Nonnegative Tensor Factorizations
Samantha Hansen, Todd Plantenga, Tamara G. Kolda
Tensor factorizations with nonnegative constraints have found application in analyzing data from cyber traffic, social networks, and other areas. We consider application data best…
Exploiting Symmetry in Tensors for High Performance: Multiplication with Symmetric Tensors
Martin D. Schatz, Tze Meng Low, Robert A. van de Geijn +1
Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a d…
On Tensors, Sparsity, and Nonnegative Factorizations
Eric C. Chi, Tamara G. Kolda
Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of…
All-at-once Optimization for Coupled Matrix and Tensor Factorizations
Evrim Acar, Tamara G. Kolda, Daniel M. Dunlavy
Joint analysis of data from multiple sources has the potential to improve our understanding of the underlying structures in complex data sets. For instance, in restaurant recommend…
Making Tensor Factorizations Robust to Non-Gaussian Noise
Eric C. Chi, Tamara G. Kolda
Tensors are multi-way arrays, and the Candecomp/Parafac (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squar…
Shifted Power Method for Computing Tensor Eigenpairs
Tamara G. Kolda, Jackson R. Mayo
Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conform…
Temporal Link Prediction using Matrix and Tensor Factorizations
Daniel M. Dunlavy, Tamara G. Kolda, Evrim Acar
The data in many disciplines such as social networks, web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this paper,…
Scalable Tensor Factorizations for Incomplete Data
Evrim Acar, Tamara G. Kolda, Daniel M. Dunlavy +1
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, bibliometr…