Expanders, tropical semi-rings, and nuclear norms: oh my!
Pages 32 - 36
Abstract
Scientific computing for social and modern information networks.
References
[1]
McPherson, M., Smith-Lovin, L. and Cook, J. M. Birds of a Feather: Homophily in social networks. Annual Review of Sociology, Annual Reviews, 27,1 (2001), 415--444.
[2]
Zhou, D., Bousquet, O., Lal, T. N., Weston, J., and Schölkopf, B. Learning with Local and Global Consistency. NIPS, 2003.
[3]
Gleich, D. F. and Zhukov, L. Scalable Computing with Power-Law Graphs: Experience with Parallel PageRank. Poster. SuperComputing 2005. November 2005.
[4]
Page, L., Brin, S., Motwani, R. and Winograd, T. The PageRank Citation Ranking: Bringing Order to the Web. Stanford University, 1999.
[5]
Wang, Y., Chakrabarti, D., Wang, C., and Faloutsos, C. Epidemic spreading in real networks: An eigenvalue viewpoint. In the Proceedings of the 22nd International Symposium on Reliable Distributed Systems (Florence, Italy, Oct. 6--8). IEEE, Washington, D.C., 2003, 25--34.
[6]
Buluç, A and Gilbert, J. R. The combinatorial BLAS: Design, implementation, and applications. International Journal of High Performance Computing Applications (IJHPCA) 25, 4 (2011), 496--509.
[7]
Kang, U., Tsourakakis, C., and Faloutsos, C. PEGASUS: A peta-scale graph mining system implementation and observations. In the ICDM '09 Proceedings of the Ninth IEEE International Conference on Data Mining (Miami, FL, Dec. 6--9), IEEE, Washington, D.C., 2009, 229--238.
[8]
Kepner, J. and Gilbert, J. (Eds.) Graph Algorithms in the Language of Linear Algebra. SIAM, Philadelphia, PA, 2011.
[9]
Leskovec, J., Lang, K. J., Dasgupta, A., and Mahoney, M. W. Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters. Internet Mathematics 6,1 (2009), 29--123.
[10]
Bonchi, F., Esfandiar, P., Gleich, D. F., Greif, C., and Lakshmanan, L. V. Fast matrix computations for pairwise and columnwise commute times and Katz scores. Internet Mathematics 8, 1--2 (2012), 73--112.
[11]
Golub, G. and Meurant, G. Matrices, moments and quadrature II: How to compute the norm of the error in iterative methods. BIT Numerical Mathematic, 37, 3 (1997), 687--705.
[12]
Benzi, M. and Boito, P. Quadrature rule-based bounds for functions of adjacency matrices. Linear Algebra and its Applications, 433, 3 (2010), 637--652.
[13]
Estrada, E. and Higham, D. J. Network properties revealed through matrix functions. SIAM Review 52, 4 (2010), 696--714.
[14]
Constantine, P. G. and Gleich, D. F. Random alpha PageRank. Internet Mathematics, 6, 2 (2010), 189--236.
[15]
Gleich, D. F., Constantine, P. G., Flaxman, A. and Gunawardana, A. Tracking the random surfer: empirically measured teleportation parameters in PageRank. In the Proceedings of the 19th international conference on World Wide Web (Raleigh, NC, April 26--30). ACM, New York, 2010, 381--390.
[16]
Kolda, T. G. and Bader, B. W. Tensor decompositions and applications. SIAM Review 51, 3 (2009), 455--500.
[17]
Hillar, C. and Lim, L.-H. Most tensor problems are NP-hard. arXiv, 2009, cs.NA, 0911.1393.
[18]
Dunlavy, D. M., Kolda, T. G., and Acar, E. Temporal link prediction using matrix and tensor factorizations. ACM Transactions on Knowledge Discovery from Data 5, 2 (2011), 10:1--10:27.
[19]
Candès, E. J. and Recht, B. Exact matrix completion via convex optimization. Foundations of Computational Mathematics 9, 6 (2009), 717--772.
Index Terms
- Expanders, tropical semi-rings, and nuclear norms: oh my!
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Published: 01 March 2013
Published in XRDS Volume 19, Issue 3
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