Parallel Nonnegative CP Decomposition of Dense Tensors

TL;DR

This paper introduces a scalable parallel algorithm for nonnegative CP tensor decomposition of dense data, optimizing computation and communication to handle large-scale tensors efficiently.

Contribution

It presents a novel distributed-memory parallel algorithm with optimized MTTKRP computation and communication strategies for nonnegative CP decomposition of dense tensors.

Findings

Scales efficiently to hundreds of nodes and thousands of cores.

Faster and more general than existing parallel software.

Effective on synthetic, hyperspectral, and neuroscience data.

Abstract

The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can enforce nonnegativity of the computed low-rank factors. The principal task is to parallelize the matricized-tensor times Khatri-Rao product (MTTKRP) bottleneck subcomputation. The algorithm is computation efficient, using dimension trees to avoid redundant computation across MTTKRPs within the alternating method. Our approach is also communication efficient, using a data distribution and parallel algorithm across a multidimensional processor grid that can be tuned to minimize communication. We benchmark our software on synthetic as well as hyperspectral image and neuroscience dynamic functional connectivity data, demonstrating that our algorithm scales well to 100s of nodes (up to 4096 cores) and is faster and more general than the currently available parallel software.