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Proceedings
SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors

Abstract

Tensor based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making it an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTMc) in general sparse tensors, the Sparse Symmetric Tensor Times Same Matrix chain (S3TTMc) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. In this work, we present a novel compressed storage format CSS for sparse symmetric tensors, along with an efficient parallel algorithm for the S3TTMc operation. We theoretically establish that S3TTMc on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations. We demonstrate experimental findings that confirm these results and achieve up to 2.9× speedup on synthetic and real datasets.

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cover image Proceedings
SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)
Pages: 193 - 204
Editors: Bender Michael, Stony Brook University, USA , Gilbert John, University of California, Santa Barbara, U.S., USA , and Sullivan D. Blair, University of Utah, USA
ISBN (Online): 978-1-611976-83-0

History

Published online: 19 July 2021

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Notes

*
Georgia Institute of Technology, Atlanta, GA, USA
Pacific Northwest National Laboratory, Richland, WA, USA; William & Mary, Williamsburg, VA, USA. This research was also partially funded by the US Department of Energy under Award No. 66150 and the Laboratory Directed Research and Development program at PNNL under contract No. ND8577.
Oak Ridge National Laboratory, Oak Ridge, TN, USA. This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
§
Georgia Institute of Technology, Atlanta, GA, USA

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