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Title: 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.

Authors:
 [1];  [2]; ORCiD logo [3];  [1]
  1. Georgia Institute of Technology, Atlanta
  2. Pacific Northwest National Laboratory (PNNL)
  3. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1820807
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Conference: SIAM Conference on Applied and Computational Discrete Algorithms (ACDA) - Spokane, Washington, United States of America - 7/19/2021 8:00:00 AM-7/21/2021 8:00:00 AM
Country of Publication:
United States
Language:
English

Citation Formats

Shivakumar, Shruti, Li, Jiajia, Kannan, Ramakrishnan, and Aluru, Srinivas. Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors. United States: N. p., 2021. Web.
Shivakumar, Shruti, Li, Jiajia, Kannan, Ramakrishnan, & Aluru, Srinivas. Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors. United States.
Shivakumar, Shruti, Li, Jiajia, Kannan, Ramakrishnan, and Aluru, Srinivas. 2021. "Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors". United States. https://www.osti.gov/servlets/purl/1820807.
@article{osti_1820807,
title = {Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors},
author = {Shivakumar, Shruti and Li, Jiajia and Kannan, Ramakrishnan and Aluru, Srinivas},
abstractNote = {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.},
doi = {},
url = {https://www.osti.gov/biblio/1820807}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2021},
month = {1}
}

Conference:
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