TY - GEN

T1 - FASTEN

T2 - 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2018

AU - Du, Boxin

AU - Tong, Hanghang

N1 - Funding Information:
This material is supported by the National Science Foundation under Grant No. IIS-1651203, IIS-1715385, IIS-1743040, and CNS-1629888, by DTRA under the grant number HDTRA1-16-0017, by the United States Air Force and DARPA under contract number FA8750-17-C-0153, by the U.S. Department of Homeland Security under Grant Award Number 2017-ST-061-QA0001 and by Army Research Office under the contract number W911NF-16-1-0168. The content of the information in this document does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.
Publisher Copyright:
© 2018 Association for Computing Machinery.

PY - 2018/7/19

Y1 - 2018/7/19

N2 - The Sylvester equation offers a powerful and unifying primitive for a variety of important graph mining tasks, including network alignment, graph kernel, node similarity, subgraph matching, etc. A major bottleneck of Sylvester equation lies in its high computational complexity. Despite tremendous effort, state-of-the-art methods still require a complexity that is at least quadratic in the number of nodes of graphs, even with approximations. In this paper, we propose a family of Krylov subspace based algorithms (FASTEN) to speed up and scale up the computation of Sylvester equation for graph mining. The key idea of the proposed methods is to project the original equivalent linear system onto a Kronecker Krylov subspace. We further exploit (1) the implicit representation of the solution matrix as well as the associated computation, and (2) the decomposition of the original Sylvester equation into a set of inter-correlated Sylvester equations of smaller size. The proposed algorithms bear two distinctive features. First, they provide the exact solutions without any approximation error. Second, they significantly reduce the time and space complexity for solving Sylvester equation, with two of the proposed algorithms having a linear complexity in both time and space. Experimental evaluations on a diverse set of real networks, demonstrate that our methods (1) are up to 10, 000× faster against Conjugate Gradient method, the best known competitor that outputs the exact solution, and (2) scale up to million-node graphs.

AB - The Sylvester equation offers a powerful and unifying primitive for a variety of important graph mining tasks, including network alignment, graph kernel, node similarity, subgraph matching, etc. A major bottleneck of Sylvester equation lies in its high computational complexity. Despite tremendous effort, state-of-the-art methods still require a complexity that is at least quadratic in the number of nodes of graphs, even with approximations. In this paper, we propose a family of Krylov subspace based algorithms (FASTEN) to speed up and scale up the computation of Sylvester equation for graph mining. The key idea of the proposed methods is to project the original equivalent linear system onto a Kronecker Krylov subspace. We further exploit (1) the implicit representation of the solution matrix as well as the associated computation, and (2) the decomposition of the original Sylvester equation into a set of inter-correlated Sylvester equations of smaller size. The proposed algorithms bear two distinctive features. First, they provide the exact solutions without any approximation error. Second, they significantly reduce the time and space complexity for solving Sylvester equation, with two of the proposed algorithms having a linear complexity in both time and space. Experimental evaluations on a diverse set of real networks, demonstrate that our methods (1) are up to 10, 000× faster against Conjugate Gradient method, the best known competitor that outputs the exact solution, and (2) scale up to million-node graphs.

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U2 - 10.1145/3219819.3220002

DO - 10.1145/3219819.3220002

M3 - Conference contribution

AN - SCOPUS:85051469136

SN - 9781450355520

T3 - Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

SP - 1339

EP - 1347

BT - KDD 2018 - Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

PB - Association for Computing Machinery

Y2 - 19 August 2018 through 23 August 2018

ER -