Motivation When searching for information on the WWW, user perform a query to a search engine. The engine return, as the query’s result, a list of Web sites which usually is a huge set. So the ranking of these web sites is very important. Because much information is contained in the link-structure of the WWW, information such as which pages are linked to others can be used to augment search algorithms.
The Stochastic Approach for Link-Structure Analysis (SALSA) and the TKC Effect The PageRank Citation Ranking: Bringing Order to the Web
hubs: web pages that point to many authoritative sites
Hubs and authorities form communities, the most prominent community is called the principal community.
SALSA----Idea SALSA is based upon the theory of Markov chains, and relies on the stochastic properties of random walks performed on our collection of sites. The input to our scheme consists of a collection of sites C which is built around a topic t. Intuition suggests that authoritative sites on topic t should be visible from many sites in the subgraph induced by C. Thus, a random walk on this subgraph will visit t-authorities with high probability.
SALSA----Idea Combine the theory of random walks with the notion of the two distinct types of Web sites, hubs and authorities, and actually analyze two different Markov chains: A chain of hubs and a chain of authorities. Analyzing both chains allows our approach to give each Web site two distinct scores, a hub score and an authority score.
SALSA----Computing Now define two stochastic matrices, which are the transition matrices of the two Markov chains at interest: The hub-matrixH: The authority-matrixÃ :
SALSA the principal community of authorities(hubs) found by the SALSA will be composed of the sites whose entries in the principal eigenvector of A (H) are the highest.
SALSA----Conclusion SALSA is a new stochastic approach for link structure analysis, which examines random walks on graphs derived from the link structure. The principal community of authorities(hubs) corresponds to the sites that are most frequently visited by the random walk defined by the authority(hub) Markov chain.
The PageRank Citation Ranking:Bringing Order to the Web Larry Page etc. Stanford University
PageRank----Idea Every page has some number of forward links(outedges) and backlinks(inedges)
PageRank----Idea Two cases PageRank is interesting: Web pages vary greatly in terms of the number of backlinks they have. For example, the Netscape home page has 62,804 backlinks compared to most pages which have just a few backlinks. Generally, highly linked pages are more “important” than pages with few links.
PageRank----Idea Backlinks coming from important pages convey more importance to a page. For example, if a web page has a link off the yahoo home page, it may be just one link but it is a very important one. A page has high rank if the sum of the ranks of its backlinks is high. This covers both the case when a page has many backlinks and when a page has a few highly ranked backlinks.
PageRank----Definition u: a web page Fu: set of pages u points to Bu: set of pages that point to u Nu=|Fu|: the number of links from u c: a factor used for normalization The equation is recursive, but it may be computed by starting with any set of ranks and iterating the computation until it converges.
PageRank----definition A problem with above definition: rank sink If two web pages point to each other but to no other page, during the iteration, this loop will accumulate rank but never distribute any rank.
PageRank----definition Definition modified: E(u) is some vector over the web pages(for example uniform, favorite page etc.) that corresponds to a source of rank. E(u) is a user designed parameter.