Social Mining Concept of Frequent Link Experimental results Conclusion and Perspectives Vers une Analyse Conceptuelle des Réseaux Sociaux Erick Stattner Martine Collard Laboratory of Mathematics and Computer Science (LAMIA) University of the French West Indies and Guiana, France MARAMI 2012 Erick Stattner, Martine Collard MARAMI 2012 1 / 27
Social Mining Concept of Frequent Link Experimental results Conclusion and Perspectives Motivation Social Mining “ New Science of Networks ” focuses on interactions between entities and investigates new methods and techniques Knowledge extraction from data on real world phenomena studied through interactions among individuals Issues New data mining techniques: Link Mining (Node classification, Link-based Clustering, Link prediction, Frequent patterns...) Attributed graph mining (Cohesive sub-graphs, Summarization, ...) Erick Stattner, Martine Collard MARAMI 2012 2 / 27
Social Mining Concept of Frequent Link Experimental results Conclusion and Perspectives Data Mining Task Context: Search for frequent patterns to answer to questions like : ◮ What are the groups of nodes the most connected? ◮ What are the nodes properties the most frequently found in connection? Contribution: Search for Frequent Links in Social Networks ◮ between groups of nodes sharing internal common properties ◮ by combining network structure and node attribute values b b b r b r b b r b r r b b Frequent link (b,r) Erick Stattner, Martine Collard MARAMI 2012 3 / 27
Social Mining Concept of Frequent Link Frequent pattern discovery Experimental results Node clustering Conclusion and Perspectives Outline 1 Social Mining Frequent pattern discovery Node clustering Concept of Frequent Link 2 Experimental results 3 Conclusion and Perspectives 4 Erick Stattner, Martine Collard MARAMI 2012 4 / 27
Social Mining Concept of Frequent Link Frequent pattern discovery Experimental results Node clustering Conclusion and Perspectives Pattern Mining in Social Networks Current Methods Main methods: Link prediction Frequent pattern discovery Node clustering Formal concept analysis Erick Stattner, Martine Collard MARAMI 2012 5 / 27
Social Mining Concept of Frequent Link Frequent pattern discovery Experimental results Node clustering Conclusion and Perspectives Pattern Mining in Social Networks Frequent pattern discovery Frequent pattern discovery: pattern = subgraph search for subgraphs occuring frequently into a large network into a set of networks X 7. X Y X 1. Y X Y X 10. Y Y 2. 6. X X Y X Z 4. 8. X Z Z X 11. Y 3. 9. Z X Z 5. Z X Erick Stattner, Martine Collard MARAMI 2012 6 / 27
Social Mining Concept of Frequent Link Frequent pattern discovery Experimental results Node clustering Conclusion and Perspectives Pattern Mining in Social Networks Node clustering Node clustering: based on links to detect subgraphs or "communities" objective: identifying groups of nodes densely connected into the network by maximizing intra-cluster links while minimizing inter-cluster links Erick Stattner, Martine Collard MARAMI 2012 7 / 27
Social Mining Concept of Frequent Link Frequent pattern discovery Experimental results Node clustering Conclusion and Perspectives Pattern Mining in Social Networks Hybrid Node clustering Hybrid node clustering: based on links and on node attributes values objective: identifying groups of nodes that share common contacts Erick Stattner, Martine Collard MARAMI 2012 8 / 27
Social Mining Concept of Frequent Link Frequent pattern discovery Experimental results Node clustering Conclusion and Perspectives Formal concept analysis Formal concept of links: based on links and on nodes objective: identifying groups of nodes that share common contacts Erick Stattner, Martine Collard MARAMI 2012 9 / 27
Social Mining Concept of Frequent Link Frequent pattern discovery Experimental results Node clustering Conclusion and Perspectives Pattern Mining in Social Networks Observation Current methods mainly use network structure often ignore nodes properties Concept of frequent link combines information both from links and from node attributes values represents a regularity involving two groups of nodes that share internal common characteristics % % Erick Stattner, Martine Collard MARAMI 2012 10 / 27
Social Mining Definition Concept of Frequent Link Knowledge extracted Experimental results Analogy with lattices of itemsets Conclusion and Perspectives Outline Social Mining 1 Concept of Frequent Link 2 Definition Knowledge extracted Analogy with lattices of itemsets Experimental results 3 Conclusion and Perspectives 4 Erick Stattner, Martine Collard MARAMI 2012 11 / 27
Social Mining Definition Concept of Frequent Link Knowledge extracted Experimental results Analogy with lattices of itemsets Conclusion and Perspectives Conceptual link Definition G = ( V , E ) network (directed) V defined as a relation R ( A 1 ,..., A p ) A 1 ,..., A p node attributes each node v ∈ V defined by the itemset A 1 = a 1 and ... and A p = a p or a 1 ... a p for m an itemset V m : set of nodes satisfying m sm sub-itemset of m V m ⊆ V sm ex: V abc ⊆ V ab Erick Stattner, Martine Collard MARAMI 2012 12 / 27
Social Mining Definition Concept of Frequent Link Knowledge extracted Experimental results Analogy with lattices of itemsets Conclusion and Perspectives Conceptual link Definition G = ( V , E ) network I V set of all possible itemsets on G Left-hand side link set LE m = { e ∈ E ; e = ( a , b ) a ∈ V m } Right-hand side link set RE m = { e ∈ E ; e = ( a , b ) b ∈ V m } Conceptual link ( m 1 , m 2 ) = LE m 1 ∩ RE m 2 (1) = { e ∈ E ; e = ( a , b ) a ∈ V m 1 et b ∈ V m 2 } (2) Erick Stattner, Martine Collard MARAMI 2012 13 / 27
Social Mining Definition Concept of Frequent Link Knowledge extracted Experimental results Analogy with lattices of itemsets Conclusion and Perspectives Frequent conceptual link Definition Support Support of l = ( m 1 , m 2 ) supp [( m 1 , m 2 )] = | ( m 1 , m 2 | | E | β : link support threshold ( m 1 , m 2 ) is a frequent conceptual link iff: supp [( m 1 , m 2 )] > β Erick Stattner, Martine Collard MARAMI 2012 14 / 27
Social Mining Definition Concept of Frequent Link Knowledge extracted Experimental results Analogy with lattices of itemsets Conclusion and Perspectives Frequent Links Knowledge provided Frequent Links: Provide knowledge on the groups of nodes the most connected in the social network i.e. knowledge on the properties most often connected Example: Bipartite network customer-product: m 1 : Gender=‘M’ and Interest=‘computer science’ m 2 : Category=‘Science Fiction’ and Product=‘book’ supp [( m 1 , m 2 )] = 14 % Erick Stattner, Martine Collard MARAMI 2012 15 / 27
Social Mining Definition Concept of Frequent Link Knowledge extracted Experimental results Analogy with lattices of itemsets Conclusion and Perspectives Frequent conceptual link Downward-closure property Sub and Super conceptual links ( sm 1 , sm 2 ) sub conceptual link of ( m 1 , m 2 ) ( sm 1 , sm 2 ) ⊆ ( m 1 , m 2 ) Downward-closure property if l is frequent then all its sub-links sl are also frequent if l is unfrequent then all its super-links sl are also unfrequent Erick Stattner, Martine Collard MARAMI 2012 16 / 27
Social Mining Definition Concept of Frequent Link Knowledge extracted Experimental results Analogy with lattices of itemsets Conclusion and Perspectives Maximal frequent conceptual link Definition Maximal frequent conceptual link ( m 1 , m 2 ) maximal frequent conceptual link iff ∄ l ′ frequent conceptual link such as l ⊂ l ′ . Erick Stattner, Martine Collard MARAMI 2012 17 / 27
Social Mining Definition Concept of Frequent Link Knowledge extracted Experimental results Analogy with lattices of itemsets Conclusion and Perspectives Conceptual view Lattice Extraction of maximal frequent conceptual link on G Concept lattice and search space reduction ab, ab ab, ab ab, a ab, b a, ab b, ab ab, a ab, b a, ab b, ab a, a a, b b, a b, b a, a a, b b, a b, b Φ , Φ Φ , Φ (a) (b) Erick Stattner, Martine Collard MARAMI 2012 18 / 27
Social Mining Definition Concept of Frequent Link Knowledge extracted Experimental results Analogy with lattices of itemsets Conclusion and Perspectives Conceptual view Definition β : link support threshold FL V max set of all maximal frequent conceptual links on G FL V max conceptual view of the social network G Seuil de support β Réseau Social Liens Conceptuels Vue Conceptuelle Fréquents 31% 22% 13% Erick Stattner, Martine Collard MARAMI 2012 19 / 27
Social Mining Concept of Frequent Link Testbed Experimental results Extracted patterns Conclusion and Perspectives Outline 1 Social Mining Concept of Frequent Link 2 Experimental results 3 Testbed Extracted patterns Conclusion and Perspectives 4 Erick Stattner, Martine Collard MARAMI 2012 20 / 27
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