Search (3 results, page 1 of 1)

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Abstract

We observe that the convergence patterns of pages in the PageRank algorithm have a nonuniform distribution. Specifically, many pages converge to their true PageRank quickly, while relatively few pages take a much longer time to converge. Furthermore, we observe that these slow-converging pages are generally those pages with high PageRank.We use this observation to devise a simple algorithm to speed up the computation of PageRank, in which the PageRank of pages that have converged are not recomputed at each iteration after convergence. This algorithm, which we call Adaptive PageRank, speeds up the computation of PageRank by nearly 30%.

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Abstract

As the Web continues to grow and encompass broader and more diverse sources of information, providing effective search facilities to users becomes an increasingly challenging problem. To help users deal with the deluge of Web-accessible information, we propose a search system which makes use of context to improve search results in a scalable way. By context, we mean any sources of information, in addition to any search query, that provide clues about the user's true information need. For instance, a user's bookmarks and search history can be considered a part of the search context. We consider two types of context-based search. The first type of functionality we consider is "similarity search." In this case, as the user is browsing Web pages, URLs for pages similar to the current page are retrieved and displayed in a side panel. No query is explicitly issued; context alone (i.e., the page currently being viewed) is used to provide the user with useful related information. The second type of functionality involves taking search context into account when ranking results to standard search queries. Web search differs from traditional information retrieval tasks in several major ways, making effective context-sensitive Web search challenging. First, scalability is of critical importance. With billions of publicly accessible documents, the Web is much larger than traditional datasets. Similarly, with millions of search queries issued each day, the query load is much higher than for traditional information retrieval systems. Second, there are no guarantees on the quality ofWeb pages, with Web-authors taking an adversarial, rather than cooperative, approach in attempts to inflate the rankings of their pages. Third, there is a significant amount of metadata embodied in the link structure corresponding to the hyperlinks between Web pages that can be exploitedduring the retrieval process. In this thesis, we design a search system, using the Stanford WebBase platform, that exploits the link structure of the Web to provide scalable, context-sensitive search.

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Abstract

We determine analytically the modulus of the second eigenvalue for the web hyperlink matrix used by Google for computing PageRank. Specifically, we prove the following statement: "For any matrix A=(cP + (1-c)E)**T, where P is an nxn row-stochasticmatrix, E is a nonnegative nxn rank-one row-stochastic matrix, and 0<=c<=1, the second eigenvalue of A has modulus Betrag (Lambda_sub2)<=c. Furthermore, if P has at least two irreducible closed subsets, the second eigenvalue Lambda_sub2 = c." This statement has implications for the convergence rate of the standard PageRank algorithm as the web scales, for the stability of PageRank to perturbations to the link structure of the web, for the detection of Google spammers, and for the design of algorithms to speed up PageRank.