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STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS

STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS. For CS790 Complex Network A Paper Presented by Bingdong Li 11/18/2009. Credit.

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STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS

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  1. STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS For CS790 Complex Network A Paper Presented by Bingdong Li 11/18/2009

  2. Credit Mehler, Alexander(2008) 'STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS',Applied Artificial Intelligence,22:7,619 — 683

  3. Outline • Objectives • Introduction • Wiki Graphs • Quantitative Network Analysis • Classification Examples • Conclusion

  4. Objectives • Looking for a framework for representing and classifying large complex networks • Focus on networks as a whole unit to be classified

  5. Outline • Objectives • Introduction • Wiki Graphs • Quantitative Network Analysis • Classification Examples • Conclusion

  6. Introduction • Through wiki graph considering its size, structure and complexity

  7. Introduction • Agent(A), document(B), and word network(C)

  8. Introduction • Network A, vertices denote agents whose collaborations span the edges. • Network B, vertices denote pages whose hyperlinks span the edges of the graph. • Network C, vertices denote words whose lexical associations

  9. Introduction • Hypotheses about the tripartite networks • Network correlation hypothesis(NCH): agent, document, and word networks correlate with respect to their small world property • Network separability Hypothesis(NSH): social and linguistic networks can be reliably separated by means of their topological characteristics

  10. Introduction Problems to solve • How to reliably segment and classify networks in order to map their constituents and similarity distributions • A efficient data structure for representing networks

  11. Introduction • Building blocks • A graph model expressive enough to map multilevel networks • A computational model of the similarities of instance of this graph model together with a classification algorithm in terms of Quantitative Network Analysis (QNA) • A model of the distribution of the kind of networking manifested by wikis

  12. Introduction • Overall approach • Investigate the separability of various topological features • Distinguish less informative from more informative topological characteristics

  13. Outline • Objectives • Introduction • Wiki Graphs • Quantitative Network Analysis • Classification Examples • Conclusion

  14. Wiki Graphs • Construct the Wiki graphs • Agent, document and linguistic • Three reference points • Micro-level, page-internal structure • meso-level, correspond to websites as thematically and functionally closed units of web-based communication • macro-level, topology of the corresponding wiki document network as a whole

  15. Wiki Graphs

  16. Wiki Graphs • New concepts • Generalized Tree(GT) • Labeled Typed Generalized Tree • Typed Graph(TG) • K-Partite Type Graph • Hypergraph • Realization of a Hypergraph • Directed graph induced by a directed hypergraph

  17. Wiki Graphs

  18. Wiki Graphs • A typed hypergraph as a model of a wiki document network (a) and its realization(b)

  19. Wiki Graphs • A multilevel graph stratified into three component graphs (edges between vertices of different component graphs are denoted by dashed lines)

  20. Outline • Objectives • Introduction • Wiki Graphs • Quantitative Network Analysis • Classification Examples • Conclusion

  21. Quantitative Network Analysis • Follows Quantitative Structure Analysis(QSA) • Segment the constituents of the target objects • Feature selection and validation • Feature aggregation and target object representation

  22. Quantitative Network Analysis • Mapping two input networks onto vectors of composite features as a prerequisite of validating their similiarity

  23. Quantitative Network Analysis

  24. Quantitative Network Analysis • Algorithm 1. for all F’ ε2Fdo 2. for X[F’] Λ Y[F’] do 3. for all CMjε {ClusteringMethodm|mε M} do 4. for all SkεSetOfParameterSettings(CMj) do 5. ComputeF-MeasureValue(Z[F’],CMj,Sk),Z ε {X,Y} 6. end for 7. end for 8. end for 9. end for

  25. Outline • Objectives • Introduction • Wiki Graphs • Quantitative Network Analysis • Classification Examples • Conclusion

  26. Classification Example – Wiki Corpus • Ontological separability

  27. Classification Example – Wiki Corpus • Functional separability

  28. Outline • Objectives • Introduction • Wiki Graphs • Quantitative Network Analysis • Classification Examples • Conclusion

  29. Conclusion • Presented a formal framework for representing, analyzing, and classifying complex networks on variant levels (here, linguistic networks on agent, document and lexico-grammatical units)

  30. Conclusion • The correlation of small world topologies on the level of social and textual network • The distinguishabilityof ontologically and functionally divergent networks • An approach to structure-oriented machine learning in the area of large complex networks

  31. Discussion

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