Scalable Tensor Methods for Nonuniform Hypergraphs

Aksoy, Sinan G.; Amburg, Ilya; Young, Stephen J.

doi:10.1137/23m1584472

Scalable Tensor Methods for Nonuniform Hypergraphs

Journal Article · Tue Jun 11 00:00:00 EDT 2024 · SIAM Journal on Mathematics of Data Science

DOI:https://doi.org/10.1137/23m1584472· OSTI ID:2396271

Aksoy, Sinan G. ^[1]; ^[1]; ^[1]

Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is applicable to nonuniform hypergraphs, but is prohibitively costly to form and analyze in practice. We develop tensor times same vector (TTSV) algorithms for this tensor which improve complexity from $O(n^r)$ to a low-degree polynomial in $$r$$, where $$n$$ is the number of vertices and $$r$$ is the maximum hyperedge size. Our algorithms are implicit, avoiding formation of the order $$r$$ adjacency tensor. Here, we demonstrate the flexibility and utility of our approach in practice by developing tensor-based hypergraph centrality and clustering algorithms. We also show these tensor measures offer complementary information to analogous graph-reduction approaches on data, and are also able to detect higher-order structure that many existing matrix-based approaches provably cannot.

View Accepted Manuscript (DOE)

Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 2396271

Report Number(s):: PNNL-SA--186918

Journal Information:: SIAM Journal on Mathematics of Data Science, Journal Name: SIAM Journal on Mathematics of Data Science Journal Issue: 2 Vol. 6; ISSN 2577-0187

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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Scalable Tensor Methods for Nonuniform Hypergraphs

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