# TuckerMPI: A Parallel C++/MPI Software Package for Large-scale Data Compression via the Tucker Tensor Decomposition

### Abstract

Our goal is compression of massive-scale grid-structured data, such as the multi-terabyte output of a high-fidelity computational simulation. For such data sets, we have developed a new software package called TuckerMPI, a parallel C++/MPI software package for compressing distributed data. The approach is based on treating the data as a tensor, i.e., a multidimensional array, and computing its truncated Tucker decomposition, a higher-order analogue to the truncated singular value decomposition of a matrix. The result is a low-rank approximation of the original tensor-structured data. Compression efficiency is achieved by detecting latent global structure within the data, which we contrast to most compression methods that are focused on local structure. In this work, we describe TuckerMPI, our implementation of the truncated Tucker decomposition, including details of the data distribution and in-memory layouts, the parallel and serial implementations of the key kernels, and analysis of the storage, communication, and computational costs. We test the software on 4.5 and 6.7 terabyte data sets distributed across 100s of nodes (1,000s of MPI processes), achieving compression ratios between 100 and 200,000X, which equates to 99–99.999% compression (depending on the desired accuracy) in substantially less time than it would take to even read the same dataset from a parallel file system. Moreover, we show that our method also allows for reconstruction of partial or down-sampled data on a single node, without a parallel computer so long as the reconstructed portion is small enough to fit on a single machine, e.g., in the instance of reconstructing/visualizing a single down-sampled time step or computing summary statistics. The code is available at https://gitlab.com/tensors/TuckerMPI.

Type
Publication
ACM Transactions on Mathematical Software
Date
Tags
Citation
G. Ballard, A. Klinvex, T. G. Kolda. TuckerMPI: A Parallel C++/MPI Software Package for Large-scale Data Compression via the Tucker Tensor Decomposition. ACM Transactions on Mathematical Software, Vol. 46, No. 2, Article ID 13, 31 pages, 2020. https://doi.org/10.1145/3378445

### Keywords

Tucker decomposition, tensor decomposition, higher-order singular valuedecomposition (HOSVD)

### BibTeX

@article{BaKlKo20,
author = {Grey Ballard and Alicia Klinvex and Tamara G. Kolda},
title = {{TuckerMPI}: A Parallel {C++/MPI} Software Package for Large-scale Data Compression via the {Tucker} Tensor Decomposition},
journal = {ACM Transactions on Mathematical Software},
volume = {46},
number = {2},
eid = {13},
pagetotal = {31}
month = {June},
year = {2020},
doi = {10.1145/3378445},
eprint = {1901.06043},
}