PLANC: Parallel Low Rank Approximation with Nonnegativity Constraints
Abstract
We consider the problem of lowrank 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 bottlenecks in both computation time and available memory. We propose a distributedmemory parallel computing solution to handle massive data sets, loading the input data across the memories of multiple nodes and performing efficient and scalable parallel algorithms to compute the lowrank approximation. We present a software package called PLANC (Parallel Low Rank Approximation with Nonnegativity Constraints), which implements our solution and allows for extension in terms of data (dense or sparse, matrices or tensors of any order), algorithm (e.g., from multiplicative updating techniques to alternating direction method of multipliers), and architecture (we exploit GPUs to accelerate the computation in this work).We describe our parallel distributions and algorithms, which are careful to avoid unnecessary communication and computation, show how to extend the software to include new algorithms and/or constraints, and report efficiency and scalability results for both synthetic and realworld data sets.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1909.01149
 Bibcode:
 2019arXiv190901149E
 Keywords:

 Mathematics  Numerical Analysis;
 Computer Science  Distributed;
 Parallel;
 and Cluster Computing;
 Computer Science  Mathematical Software
 EPrint:
 arXiv admin note: text overlap with arXiv:1806.07985