15-spectral_annot

15-spectral_annot -...

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CS224W: Social and Information Network Analysis re eskovec tanford University Jure Leskovec, Stanford University http://cs224w.stanford.edu
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sk: Task: Find coalitions in signed networks centives: Incentives: European chocolates! Fame Up to 10% extra credit Due: Friday midnight No late days! 11/8/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 2
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Today: 3 methods (3) Trawling: Community signatures that can be efficiently extracted (4) Spectral graph partitioning: Laplacian matrix, 2nd eigenvector (5) Overlapping communities: Clique percolation method 11/8/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3
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[Kumar et al. ‘99] arching for small communities in Web graph Searching for small communities in Web graph (1) What is the signature of a mmunity/discussion in a Web graph community/discussion in a Web graph Use this to define topics: h t th l th What the same people on the left talk about on the right 11/8/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu A dense 2 layer graph Intuition: many people all talking about the same things 4
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[Kumar et al. ‘99] ) A more well efined problem: (2) A more well defined problem: Enumerate complete bipartite subgraphs K s,t here odes where each links to the Where K s,t = s nodes where each links to the same t other nodes 11/8/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 5
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[Kumar et al. ‘99] o points: Two points: (1) The signature of a community/discussion ) omplete bipartite bgraph (2) Complete bipartite subgraph K s,t K s,t = graph on s nodes, each links to the same t other nodes Plan: (A) From (2) get back to (1): Via: Any dense enough graph contains a smaller K s,t as a subgraph (B) How do we solve (2) in a giant graph? hat similar problems have been solved on big non aph data? What similar problems have been solved on big non graph data? (3) Frequent itemset enumeration [Agrawal Srikant ‘99] 11/8/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6
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[Agrawa Srikant ‘99] arketbasket alysis: Marketbasket analysis: What items are bought together in a store? tting: Setting: Universe U of n items m subsets of U : S 1 , S 2 , …, S m U ( S i is a set of items one person bought) equency threshold Frequency threshold f Goal: d ll bt t f t Find all subsets T s.t. T S i of f sets S i (items in T were bought together f times) 11/8/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 7
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xample: Example: Universe of items: U={1,2,3,4,5} {,,,,} Itemsets: S 1 ={1,3,5}, S 2 ={2,3,4}, S 3 ={2,4,5}, S 4 ={3,4,5}, S 5 ={1,3,4,5}, S 6 ={2,3,4,5} Minimum support: 3 f =3 Algorithm: Build up the lists sight: r a frequent set of size ll Insight: for a frequent set of size k , all its subsets are also frequent 11/8/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 8
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15-spectral_annot -...

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