2008 have explored ways to test the statistical

Info icon This preview shows pages 26–28. Sign up to view the full content.

(2008) have explored ways to test the statistical significance of the output of graph partitioning algorithms. Their methods attempt to determine whether a model which lacks structure could equally well explain the group structure inferred from the data. These approaches, though distinct from one another, are both akin to performing a permutation test – a method known to be effective when applied to more general cases of clustering. Carley and Banks (1993) apply this exact idea to test for structure when group memberships are given. Other researchers have attempted a more empirical approach to the problem of partition evaluation by adopting a metric to measure the distance between found and “true” partitions. Such distances are then examined for a variety of data sets and simulated cases for which the true Copyright © 2014. Imperial College Press. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 2/16/2016 3:37 AM via CGC-GROUP OF COLLEGES (GHARUAN) AN: 779681 ; Heard, Nicholas, Adams, Niall M..; Data Analysis for Network Cyber-security Account: ns224671
Image of page 26

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Inference for Graphs and Networks 27 partition is assumed known. In this vein Danon et al. (2005) specified an explicit probability model for structure and compared how well different graph partitioning schemes recovered the true subgroups of data, rank- ing them by both execution time as well as average distance between true and found partitions. Gustafsson et al. (2006) performed a similar com- parison, along with a study of differences in “found” partitions between algorithms for several well-known data sets, including the karate club data of Section 1.4.1. They found that standard clustering algorithms (e.g., k -means) sometimes outperform more specialized network partition algo- rithms. Finally, Fortunato and Barth´ elemy (2007) have undertaken theoret- ical investigations of the sensitivity and power of a particular partitioning algorithm to detect subgroups below a certain size. References Adamic, L. A. and Huberman, B. A. (2000). Power-law distribution of the World Wide Web, Science 287 , p. 2115. Airoldi, E. M., Blei, D. M., Fienberg, S. E. and Xing, E. P. (2007). Combining stochastic block models and mixed membership for statistical network anal- ysis, in E. M. Airoldi, D. M. Blei, S. E. Fienberg, A. Goldenberg, E. P. Xing and A. X. Zheng (eds), Papers from the ICML 2006 Workshop on Statistical Network Analysis (Springer, Berlin), pp. 57–74. Airoldi, E. M., Blei, D. M., Fienberg, S. E. and Xing, E. P. (2008). Mixed mem- bership stochastic block models, J. Machine Learn. Res. 9 , pp. 1981–2014. Altman, D. G., Lausen, B., Sauerbrei, W. and Schumacher, M. (1994). Dangers of using “optimal” cutpoints in the evaluation of prognostic factors, J. Natl.
Image of page 27
Image of page 28
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '12
  • Kushal Kanwar
  • Graph Theory, Statistical hypothesis testing, Imperial College Press, applicable copyright law

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern