Sparse Symmetric Format for Tucker Decomposition

Journal Article · Wed Mar 29 00:00:00 EDT 2023 · IEEE Transactions on Parallel and Distributed Systems

DOI:https://doi.org/10.1109/tpds.2023.3263124· OSTI ID:1997626

Shivakumar, Shruti ^[1]; Li, Jiajia ^[2]; Kannan, Ramakrishnan ^[3]; Aluru, Srinivas ^[1]

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1. Georgia Institute of Technology, Atlanta, GA (United States)
2. North Carolina State University, Raleigh, NC (United States)
3. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

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 them an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTM c ) in general sparse tensors, the $$\underline{S}$$ parse $$\underline{S}$$ ymmetric $$\underline{T}$$ ensor $$\underline{T}$$ imes $$\underline{S}$$ ame $$\underline{M}$$ atrix $$\underline{c}$$ hain (S ³ TTM c ) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. We present the novel Compressed Sparse Symmetric (CSS) format for sparse symmetric tensors, along with an efficient parallel algorithm for the S ³ TTM c operation. We theoretically establish that S ³ TTM c on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations, and visualize the variation of the performance gap over the parameter space. We demonstrate experimental findings that confirm these results and achieve up to 2.72× speedup on synthetic and real datasets. The scaling of the algorithm on different test architectures is also showcased to highlight the effect of machine characteristics on algorithm performance.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1997626
• Journal Information: IEEE Transactions on Parallel and Distributed Systems, Journal Name: IEEE Transactions on Parallel and Distributed Systems Journal Issue: 6 Vol. 34; ISSN 1045-9219
• Publisher: IEEE
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
compressed storage
sparse tensors
symmetric tensors
tensor times matrix chain