Grey Ballard
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View article: Improved Analysis of Khatri-Rao Random Projections and Applications
Improved Analysis of Khatri-Rao Random Projections and Applications Open
Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard G…
View article: Brief Announcement: Minimizing Communication for Parallel Symmetric Tensor Times Same Vector Computation
Brief Announcement: Minimizing Communication for Parallel Symmetric Tensor Times Same Vector Computation Open
International audience
View article: Minimizing Communication for Parallel Symmetric Tensor Times Same Vector Computation
Minimizing Communication for Parallel Symmetric Tensor Times Same Vector Computation Open
In this article, we focus on the parallel communication cost of multiplying the same vector along two modes of a $3$-dimensional symmetric tensor. This is a key computation in the higher-order power method for determining eigenpairs of a $…
View article: Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations
Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations Open
In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix wi…
View article: Randomized Algorithms for Symmetric Nonnegative Matrix Factorization
Randomized Algorithms for Symmetric Nonnegative Matrix Factorization Open
Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algor…
View article: Randomized Algorithms for Symmetric Nonnegative Matrix Factorization
Randomized Algorithms for Symmetric Nonnegative Matrix Factorization Open
Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more sca…
View article: Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation
Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation Open
International audience
View article: Sequential and Shared-Memory Parallel Algorithms for Partitioned Local Depths
Sequential and Shared-Memory Parallel Algorithms for Partitioned Local Depths Open
In this work, we design, analyze, and optimize sequential and shared-memory parallel algorithms for partitioned local depths (PaLD). Given a set of data points and pairwise distances, PaLD is a method for identifying strength of pairwise r…
View article: AminerMag X Dataset
AminerMag X Dataset Open
A subset of the Microsoft Open Academic Graph (OAG), a dataset consisting of a unification of the Microsoft Academic Graph (MAG) and ArnetMiner (AMiner) academic graphs each respectively containing 166,192,182 and 154,771,162 papers. From …
View article: AminerMag S Dataset
AminerMag S Dataset Open
A subset of the Microsoft Open Academic Graph (OAG), a dataset consisting of a unification of the Microsoft Academic Graph (MAG) and ArnetMiner (AMiner) academic graphs each respectively containing 166,192,182 and 154,771,162 papers. From …
View article: AminerMag S Dataset
AminerMag S Dataset Open
A subset of the Microsoft Open Academic Graph (OAG), a dataset consisting of a unification of the Microsoft Academic Graph (MAG) and ArnetMiner (AMiner) academic graphs each respectively containing 166,192,182 and 154,771,162 papers. From …
View article: AminerMag X Dataset
AminerMag X Dataset Open
A subset of the Microsoft Open Academic Graph (OAG), a dataset consisting of a unification of the Microsoft Academic Graph (MAG) and ArnetMiner (AMiner) academic graphs each respectively containing 166,192,182 and 154,771,162 papers. From …
View article: Distributed-Memory Parallel JointNMF
Distributed-Memory Parallel JointNMF Open
Joint Nonnegative Matrix Factorization (JointNMF) is a hybrid method for mining information from datasets that contain both feature and connection information. We propose distributed-memory parallelizations of three algorithms for solving …
View article: CP decomposition for tensors via alternating least squares with QR decomposition
CP decomposition for tensors via alternating least squares with QR decomposition Open
The CP tensor decomposition is used in applications such as machine learning and signal processing to discover latent low‐rank structure in multidimensional data. Computing a CP decomposition via an alternating least squares (ALS) method r…
View article: Parallel Memory-Independent Communication Bounds for SYRK
Parallel Memory-Independent Communication Bounds for SYRK Open
In this paper, we focus on the parallel communication cost of multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK). SYRK requires half the computation of general matrix multiplication because of the symmetry o…
View article: Randomized Algorithms for Rounding in the Tensor-Train Format
Randomized Algorithms for Rounding in the Tensor-Train Format Open
The tensor-train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential equati…
View article: Parallel Randomized Tucker Decomposition Algorithms
Parallel Randomized Tucker Decomposition Algorithms Open
The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two a…
View article: Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation
Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation Open
Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower boun…
View article: Brief Announcement
Brief Announcement Open
International audience
View article: Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds
Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds Open
Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…
View article: Parallel Algorithms for Tensor Train Arithmetic
Parallel Algorithms for Tensor Train Arithmetic Open
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
View article: CP Decomposition for Tensors via Alternating Least Squares with QR Decomposition
CP Decomposition for Tensors via Alternating Least Squares with QR Decomposition Open
The CP tensor decomposition is used in applications such as machine learning and signal processing to discover latent low-rank structure in multidimensional data. Computing a CP decomposition via an alternating least squares (ALS) method r…
View article: Randomized algorithms for rounding in the Tensor-Train format
Randomized algorithms for rounding in the Tensor-Train format Open
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential equati…
View article: Parallel Tucker Decomposition with Numerically Accurate SVD
Parallel Tucker Decomposition with Numerically Accurate SVD Open
Tucker decomposition is a low-rank tensor approximation that generalizes a truncated matrix singular value decomposition (SVD). Existing parallel software has shown that Tucker decomposition is particularly effective at compressing terabyt…
View article: PLANC
PLANC Open
We consider the problem of low-rank approximation of massive dense nonnegative tensor data, for example, to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting bottlen…
View article: Parallel Algorithms for Tensor Train Arithmetic
Parallel Algorithms for Tensor Train Arithmetic Open
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
View article: Distributed-Memory Parallel Symmetric Nonnegative Matrix Factorization
Distributed-Memory Parallel Symmetric Nonnegative Matrix Factorization Open
We develop the first distributed-memory parallel implementation of Symmetric Nonnegative Matrix Factorization (SymNMF), a key data analytics kernel for clustering and dimensionality reduction. Our implementation includes two different algo…
View article: Pixel Similarity
Pixel Similarity Open
This dataset consists of pixel-pixel similarity matrices that were created from large satellite images. These matrices can be factored to produce pixel embeddings for various image segmentation tasks.