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What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
What the matrix can tell us about the social network.
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What the matrix can tell us about the social network.

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In this talk, I give a high level picture of my research about how looking at social network problems as matrix computations is a productive line of work.

In this talk, I give a high level picture of my research about how looking at social network problems as matrix computations is a productive line of work.

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  • 1. THE MATRIX & THESOCIAL NETWORKDAVID F. GLEICHPURDUE UNIVERSITY, COMPUTER SCIENCE
  • 2. RÉSUMÉUndergraduate Harvey Mudd College Joint CS/Math!Internships Microsoft and Yahoo!!Graduate Stanford University ! "Computational and Mathematical Engineering!Internships Intel, Yahoo!, Microsoft, Library of Congress!Postdoc University of British Columbia!Postdoc Sandia National Laboratories "! "John von Neumann Fellow !!Faculty Purdue University Computer Science!!
  • 3. Copyright Warner Brothers
  • 4. “The series depicts acyberpunk story incorporating numerous references to philosophical and religious ideas.” --Wikipedia Copyright Warner Brothers
  • 5. Copyright Warner Brothers
  • 6. Physical simulation Copyright Warner Brothers
  • 7. Matrixcomputations are the heart (and not brains) of modern physical simulation.
  • 8. Matrix computations Physics Statistics Engineering Graphics Databases …
  • 9. Matrix computations 2 3 A1,1 A1,2 ··· A1,n 6 . 7 . 7 6 A2,1 A2,2 ··· . 7 A=6 . 6 7 4 . .. .. . . . Am 1,n 5 Am,1 ··· Am,n 1 Am,n Ax = b min kAx bk Ax = xLinear systems Least squares Eigenvalues
  • 10. “… greed, obsession,unpredictability … ” --Wikipedia Copyright Columbia Pictures
  • 11. The power of connections
  • 12. The matrix is a powerful and productive paradigm for studying networks of connections.
  • 13. Matrix computations 2 3 A1,1 A1,2 ··· A1,n 6 . 7 . 7 6 A2,1 A2,2 ··· . 7 A=6 . 6 7 4 . .. .. . . . Am 1,n 5 Am,1 ··· Am,n 1 Am,n Ax = b min kAx bk Ax = xLinear systems Least squares Eigenvalues
  • 14. A new matrix-based sensitivity analysis of Google’s PageRank. Presented at" WAW2007, WWW2010 RAPr on Wikipedia E [x(A)] Std [x(A)] Published in the United States United States J. Internet Mathematics C:Living people C:Living people France C:Main topic classif. Led to new results on United Kingdom C:Contentsuncertainty quantification in Germany C:Ctgs. by country physical simulations England United Kingdompublished in SIAM J. Matrix Canada France Analysis and SIAM J. Japan C:Fundamental Scientific Computing. Poland England Australia C:Ctgs. by topic Patent Pending Gleich (Stanford) Improved web-spam detection! Random sensitivity Ph.D. Defense 23 / 41 Collaborators Paul Constantine, Gianluca Iaccarino (physical simulation)
  • 15. Fast matrix computations for " Tweet aloKatz scores and commute times. – MAIN RESULTS SLIDE THREE Presented at" WAW2010 Published in the J. Internet Mathematics Reduced computation time by orders of magnitude! David F. Gleich (Sandia) ICME la/opt seminarCollaborators Chen Greif, Laks V. S. Lakshmanan, Francesco Bonchi, Pooya Esfandiar
  • 16. EK-HENG LIM · U. CHICAGO Reduction tree Tall-and-skinny QR factorizations (Red) S(2) The number of (Red) (Red) S(2) shuffleABILITY reducers and S(1) A on MapReduce architectures.matrix completion results are recovery the-ow when the solution of the convex heuristic solution. Using a recent matrix-completion iterations to use Network AlignmentDavid Gross (2010), we prove:Let s be centered, i.e., = 0. Let Y = sT e j David Gleich (Sandia) Iteration 1 MapReduce 2011 Iter 2 Iter 3 15/ere = m x s2 / (sT s) and = ((m x s ) Also, let r Algorithms for large sparse ⇢ H be a random set Square of elements O(2n (1 + )(log n)2 ) where = m x((n +en the solution of s kXk network alignment problems.o tr ce(X W ) = tr ce(( Y) W ), t W 2t with probability at least 1 n . A L BY “About n log n comparisons for recovery.” weight overlap theorem is not useful because we only need upper bound 60,120t of measurements from Y to generate the nstead, this theorem gives intuition for15,214 NetAlignBP 56,361 17,571 the solving an LP – 1 day iterative updates Overlapping clusters for distri- (think matrix-vectory probem. We test this by generating a skew- multiplies) – 10 min trix Y from a score vector s, and determine rounded LP 46,270mparisons we need before the we are able to 17,251 solving an LP –1 day buted network computations. ector s For these results, algorithm. We vertices, B is approx 300k vertices, and L is Note using the SVP A is approx 200k then do 5m edges. This setup yields a 5m variable integer QP.eriment by adding Gaussian noise to the mea-e find aDavid F. Gleich (UBC) at n log n measurements. threshold Sandia 2 / 35 ry Noisy recovery 0.05 2n log(n) 6n log(n) Rank aggregation via skew- 0.04 Noise level 5n 0.03 0.02 symmetric matrix completion. 2n log(n) 6n log(n) 0.01 5n 3 4 0 10 10 200 1000 5000 Samples Samples C RESULTS
  • 17. My research Or we " Presentations on my website can " Implementations on my website chat " Even more on my website! this " week. www.cs.purdue.edu/homes/dgleich @dgleich on Twitter

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