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15 networks lecture 7 link structure1 for a dierent

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Unformatted text preview: the authority of a page on the topic: First, collect a large sample of pages that are relevant to the query as determined by a classical, text-only, information retrieval approach. Pick the webpage that receives the greatest number of in-links (score) from these pages. 15 Networks: Lecture 7 Link Structure–1 For a different query, say “newspaper”, the “most important page” seems less obvious, i.e., you get a high score for a mix of prominent newspapers, as well as for pages that are going to receive many links no matter what the query is (such as Yahoo, Facebook, Amazon). Image by MIT OpenCourseWare. Adapted from Easley, David, and Jon Kleinberg. Networks, Crowds, and Markets: Reasoning about a Highly Connected World. New York, NY: Cambridge University Press, 2010. ISBN: 9780521195331. Figure: Counting in-links to pages for the query “newspapers”. 16 Image by MIT OpenCourseWare. Adapted from Easley, David, and Jon Kleinberg. Networks, Crowds, and Markets: Reasoning about a Highly Connected World. New York, NY: Cambridge University Press, 2010. ISBN: 9780521195331. Networks: Lecture 7 Hubs and Authorities–1 This suggests a ranking procedure which is defined in terms of two kinds of nodes: Authorities: The prominent highly endorsed answers to the queries (nodes that are pointed to by highly ranked nodes) Hubs: High-value lists (nodes that point to highly ranked nodes) For each page p , we are trying to estimate its value as a potential authority and as a potential hub, so we assign it to numerical values b (p ) (for authority weight) and h(p ) (for hub weight). Let A denote the n × n adjacency matrix, i.e., Aij = 1 if there is a link from node i to node j . The authority and hub weights then satisfy: h (i ) = ∑ Aij b (j ) for all i , ∑ Aij h(i ) for all j . j b (j ) = i 18 Networks: Lecture 7 Hubs and Authorities–2 This can be written in matrix-vector notation as: h = Ab , b T = hT A or b = AT h, where b T (or AT ) denotes the transpose of vector b (or matrix A). This yields an iterativ...
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