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In the original form of PageRank, the sum of PageRank over all pages was the total number of pages on the web at that time, so each page in this example would have an initial value of 1. However, later versions of PageRank, and the remainder of this section, assume a probability distribution between 0 and 1.
Numeric examples of PageRank values in a small graph with a damping factor of 0.85. The exact solution is: = ... Page Rank; Usage on bn.wikipedia.org
Fig.1. Google matrix of Wikipedia articles network, written in the bases of PageRank index; fragment of top 200 X 200 matrix elements is shown, total size N=3282257 (from [1]) A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links between pages.
Ranking of query is one of the fundamental problems in information retrieval (IR), [1] the scientific/engineering discipline behind search engines. [2] Given a query q and a collection D of documents that match the query, the problem is to rank, that is, sort, the documents in D according to some criterion so that the "best" results appear early in the result list displayed to the user.
For example, the number of words in a query. Some examples of features, which were used in the well-known LETOR dataset: TF, TF-IDF, BM25, and language modeling scores of document's zones (title, body, anchors text, URL) for a given query; Lengths and IDF sums of document's zones; Document's PageRank, HITS ranks and their variants.
The PageRank algorithm instead analyzes human-generated links assuming that web pages linked from many important pages are also important. The algorithm computes a recursive score for pages, based on the weighted sum of other pages linking to them. PageRank is thought to correlate well with human concepts of importance. In addition to PageRank ...
Both Democratic and Republican administrations kept up work with for-profit prisons on immigration — the Biden administration, for example, deported more people than Trump's first administration ...
HITS, like Page and Brin's PageRank, is an iterative algorithm based on the linkage of the documents on the web. However it does have some major differences: It is processed on a small subset of ‘relevant’ documents (a 'focused subgraph' or base set), instead of the set of all documents as was the case with PageRank.