A3 approximate inference procedures in most cases of

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A.3. Approximate Inference Procedures In most cases of practical interest, and in particular for large network data sets, model likelihoods cannot be maximized in a computationally feasi- ble manner, and researchers must appeal to a heuristic that yields some approximately maximized quantity. With this goal in mind, the idea of likelihood maximization has been subsumed by the idea of fast graph par- titioning described in Section 1.3.2, as it is the process of determining group membership which typically poses the most computational challenges. The invention of new algorithms that can quickly partition large graphs is clearly of great utility here. A.3.1. Algorithmic approaches Computer scientists and physicists have long been active in the creation of new graph partitioning algorithms. In addition to techniques such as spectral bisection, many researchers have also noted that the inherently 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
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26 B. P. Olding and P. J. Wolfe sparse nature of most real-world adjacency structures enables faster imple- mentations of spectral methods (see, e.g., White and Smyth (2005)). Researchers have sought to also incorporate graph partitioning concepts that allow for multiple partitions of varying sizes. Some researchers, such as Eckmann and Moses (2002) and Radicchi et al. (2004), have attempted to use strictly local statistics to aid in the clustering of nodes into multi- ple partitions. Girvan and Newman (2002) focused in contrast on global statistics, by way of measures of the centrality of a node relative to the rest of the graph. This line of reasoning eventually resulted in the introduction of modularity (Newman, 2006) as a global statistic to relate the observed number of edges between groups to their expected number under the con- figuration model outlined in Section A.1. Spectral clustering methods can also be applied to the task of approximately maximizing modularity, in a manner that enables both group size and number to vary. A wide variety of alternative maximization approaches have been applied as well: Both Wang et al. (2007) and Brandes et al. (2008) review the computational difficulties associated with maximization of the modularity statistic, and relate this to known combinatorial optimization problems. Fortunato and Castellano (2007) review many recently proposed maximization routines and contrast them with traditional methods. A.3.2. Evaluation of efficacy Approximate procedures in turn require some way to evaluate the depar- ture from exact likelihood maximization. Thus far, a clear way to eval- uate partitions found through the various heuristics cited above has not yet emerged, though many different approaches have been proposed. Both Massen and Doye (2006) and Karrer et al.
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  • Spring '12
  • Kushal Kanwar
  • Graph Theory, Statistical hypothesis testing, Imperial College Press, applicable copyright law

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