STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS
For CS790 Complex NetworkA Paper Presented by Bingdong Li
11/18/2009
Credit
Mehler, Alexander(2008) 'STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS',Applied Artificial Intelligence,22:7,619 — 683
Outline
• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion
Objectives
• Looking for a framework for representing and classifying large complex networks
• Focus on networks as a whole unit to be classified
Outline
• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion
Introduction
• Through wiki graph considering its size, structure and complexity
Introduction
• Agent(A), document(B), and word network(C)
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
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
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
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
Introduction
• Overall approach– Investigate the separability of various topological
features– Distinguish less informative from more informative
topological characteristics
Outline
• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion
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
Wiki Graphs
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
Wiki Graphs
Wiki Graphs
• A typed hypergraph as a model of a wiki document network (a) and its realization(b)
Wiki Graphs
• A multilevel graph stratified into three component graphs (edges between vertices of different component graphs are denoted by dashed lines)
Outline
• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion
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
Quantitative Network Analysis
• Mapping two input networks onto vectors of composite features as a prerequisite of validating their similiarity
Quantitative Network Analysis
Quantitative Network Analysis
• Algorithm1. for all F’ ε 2F do2. for X[F’] Λ Y[F’] do3. for all CMj ε {ClusteringMethodm|m ε M} do4. for all Sk ε SetOfParameterSettings(CMj) do5. ComputeF-MeasureValue(Z[F’],CMj,Sk),Z ε {X,Y}6. end for7. end for8. end for9. end for
Outline
• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion
Classification Example – Wiki Corpus
• Ontological separability
Classification Example – Wiki Corpus
• Functional separability
Outline
• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion
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)
Conclusion
• The correlation of small world topologies on the level of social and textual network
• The distinguishability of ontologically and functionally divergent networks
• An approach to structure-oriented machine learning in the area of large complex networks
Discussion