Bruno Martins. 1 st Semester 2012/2013

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1 Link Analysis Departamento de Engenharia Informática Instituto Superior Técnico 1 st Semester 2012/2013 Slides baseados nos slides oficiais do livro Mining the Web c Soumen Chakrabarti.

2 Outline

3 Outline

4 Traditional IR Traditional IR systems: Worth of a document regarding a query is intrinsic to the document. Documents are self-contained units Documents are descriptive and truthful

5 Web IR The World Wide Web is a shifting universe Indefinitely growing Non-textual content Invisible keywords Documents are not self-complete Most web queries 2 words long Hyperlinked

6 The Web as a Graph Web as a hyperlink graph Evolves organically, No central coordination, Yet shows global and local properties An example of social network

7 Graph structure of the Web

8 Graph structure of the Web

9 Network Analysis Studies properties related to connectivity and distances in graphs Example applications: Epidemiology Identifying a few nodes to be removed to significantly increase average path length between pairs of nodes Citation analysis Identifying influential or central papers

10 The Web as a Network Hypermedia is a social network network theory Extensive research applying graph notions Centrality and prestige Co-citation (relevance judgment) Applications Web search:, Google Classification and topic distillation

11 Exploiting the link structure Ranking search results Keyword queries not selective enough Use graph notions of popularity/prestige and Supervised and unsupervised learning Hyperlinks and content are strongly correlated Can be used to classify documents Can be used to cluster documents

12 Outline

13 Document citation graph Node adjacency matrix E E[i, j] = 1 iff document i cites document j, and zero otherwise. Prestige vector over all nodes: p Prestige p[v] associated with every node v

14 Centrality Graph-based notions of centrality Distance d(u,v) = number of links between u and v Radius of node u is Center of the graph is r(u) = max d(u,v) v center = argmin r(u) u Example: Influential papers in an area of research by looking for papers u with small r(u)

15 Co-citation Documents v and w are said to be co-cited by u if document u cites documents v and w If E is the document citation matrix E T E is the co-citation index matrix Indicator of relatedness between every v and w Example use: clustering Using above pair-wise relatedness measure in a clustering algorithm

16 Example clustering

17 Link-based Ranking Strategies Goal: Leverage the abundance problems inherent in broad queries Google s ing Measure of prestige with every page on web : Hyperlink Induced Topic Search Use query to select a sub-graph from the Web. Identify hubs and authorities in the sub-graph

18 Link Model Each page is a node without any textual properties Each hyperlink is an edge connecting two nodes with possibly only a positive edge weight property Some preprocessing procedure outside the scope of the algorithm may be used to choose what sub-graph of the Web to analyze, in response to a query

19 Outline

20 Overview of Pre-computes a rank-vector Provides a-priori (offline) importance estimates for all pages on Web Independent of search query In-degree prestige Not all votes are worth the same Prestige of a page is the sum of prestige of citing pages: p = Ep Pre-compute query independent prestige score Query time: prestige scores used in conjunction with query-specific IR scores

21 Assumption: the prestige of a page is proportional to the sum of the prestige scores of pages linking to it Idea of a random surfer on a strongly connected web graph

22 The algorithm: E is adjacency matrix of the Web { 1 iff there is a link from u to v E[u, v] = 0 otherwise The out-degree of node u is given by N u = v E[u, v] Start with an initial prestige vector p 0 [u] Compute p i+1 [v] = (u,v) E p i [u] N u

23 Convergence Convergence to stationary distribution of the normalized adjacency matrix L p is principal eigenvector of L Convergence criteria L is irreducible there is a directed path from every node to every other node L is aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph

24 Problems of Convergence Web graph is not strongly connected Only a fourth of the graph is! Web graph is not aperiodic Rank-sinks Pages without out-links Directed cyclic paths

25 A simple fix Two way choice at each node With a certain probability d (0.1 < d < 0.2), the surfer jumps to a random page on the Web With probability 1 d the surfer decides to choose, uniformly at random, an out-neighbor p i+1 [v] = d N + (1 d) (u,v) E p i [u] N u

26 architecture at Google Ranking of pages more important than exact values of p Convergence of page ranks in 52 iterations for a crawl with 322 million links. Pre-compute and store the of each page. independent of any query or textual content. Ranking scheme combines with textual match Unpublished Many empirical parameters, human effort and regression testing.

27 Outline

28 : Hypertext Induced Topic Selection Relies on query-time processing To select base set V q of links for query q constructed by selecting a sub-graph R from the Web (root set) relevant to the query selecting any node u which neighbors any r R via an inbound or outbound edge (expanded set) To deduce hubs and authorities that exist in a sub-graph of the Web Every page u has two distinct measures of merit, its hub score h[u] its authority score a[u] Recursive quantitative definitions of hub and authority scores

29 Hubs and Authorities Hub A page is a good hub if it contains links to many good authority pages Authority A page is a good authority if it is pointed to by many good hubs Authority pages provide good content. Hub pages provide links to the pages with good content.

30 The Algorithm

31 vs. advantage over Query-time cost is low computes an eigenvector for every query Less susceptible to localized link-spam advantage over ranking is sensitive to query has notion of hubs and authorities

32 Questions?

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