Applications </li></li></ul><li>Motivation<br />-> Need for PageRank:<br /> The Search engines store billions of web pages which overall contain trillions of web url links. So, there is a need for an algorithm that gives the most relevant pages specific to a query.<br />-> Need for Distributed Environment<br />( Map-Reduce and Distributed Storage)<br /><ul><li> Trillions of links implies huge data storage required.</li></ul> (if each url requires 0.5K, then we need over 400TB just to store URLs!) <br /><ul><li> Large data set implies large computations</li></ul>Thus, we handle above issues in our project by using a distributed cluster<br />
Applications </li></li></ul><li>Introduction<br />PageRank is a link analysis algorithm, named after Larry Page, used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinkedset of documents, such as the Worldwide Web, with the purpose of "measuring" its relative importance within the set<br />The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).<br />
Algorithm<br />Google figures that when one page links to another page, it is effectively casting a vote for the other page. The more votes that are cast for a page, the more important the page must be. Also, the importance of the page that is casting the vote determines how important the vote itself is. Google calculates a page's importance from the votes cast for it. How important each vote is also taken into account when a page's PageRank is calculated.<br />
PageRank Equation(Enhancement)<br />Solution for Cycles and If a random surfer gets bored<br />Here ‘d ‘ is known as damping factor . It represents the probability, at any step, that the person will continue surfing . The value of ‘d’ is typically kept 0.85<br />
In other words<br />In a simpler way:- <br />a page's PageRank = 0.15 /N+ 0.85 * (a "share" of the PageRank of every page that links to it) <br />"share" = the linking page's PageRank divided by the number of outbound links on the page. <br />And N=the number of documents in collection<br />The equation of PageRank shows clearly how a page's PageRank is arrived at. But what isn't immediately obvious is that it can't work if the calculation is done just once. <br />
PageRank Equation-as per the published paper :“The Anatomy of a Large-Scale Hyper textual Web Search Engine”-Sergey Brin and Lawrence Page <br />We assume page A has pages T1...Tn which point to it (i.e., are citations). The parameter d is a damping factor which can be set between 0 and 1. We usually set d to 0.85.. Also C(A) is defined as the number of links going out of page A. <br />The PageRank of a page A is given as follows: <br />PR(A) = (1-d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn)) <br />->Note that the PageRanks form a probability distribution over web pages, so the sum of all web pages’ PageRanks will be one.<br />
IssuesIn the Original Formula<br />Formula given in the in Page and Brin's paper does not supports the statement that "the sum of all PageRanks is one“<br />Hence to support the statement the formula is modified as:<br /> PR(A) = (1-d)/N + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))<br />where N=the number of documents in collection<br />
Applications </li></li></ul><li>Brief Description of Project<br />Input: <br />Data Set containing multiple records where each record contains the Url of the Page(from Url) followed by the url of a page to which it is pointing to(ToUrl).<br />Wiki_Votes.txt<br />ToUrl<br />FromUrl<br />
Brief Description of Project(Contd.)<br />Output:<br />The output file consist of records containing the url of the page(from Url), the page rank value of the page(PRValue) and the list of urls to which the page points to(ToUrlList).<br />FinalOutput.txt<br />ToUrlList<br />fromUrl<br />PRValue<br />
Module1: ConverterIssues<br />Self Loops:<br /> -handled by checking the FromUrl with ToUrl before sending it to the reduce function<br /> Dangling Pages:<br /> -handled by initializing their PRValue with 1/N and the List of ToUrls is left blank.<br />
Module2: PageRank Calculator IssuesCatch22 Situation<br />Suppose we have 2 pages, A and B, which link to each other, and neither have any other links of any kind. This is what happens:- <br />Step 1: Calculate page A's PageRank from the value of its inbound links<br />Step 2: Calculate page B's PageRank from the value of its inbound links<br /> we can't work out A's PageRank until we know B's PageRank, and we can't work out B's PageRank until we know A's PageRank. Thus the PageRank of A and B will be inaccurate.<br />
Module2: PageRank Calculator IssuesCatch22 situation (solution)<br />This problem is overcome by repeating the calculations many times. Each time produces slightly more accurate values. In fact, total accuracy can never be achieved because the calculations are always based on inaccurate values.<br />The number of iterations should be sufficient to reach a point where any further iterations wouldn't produce enough of a change to the values to matter.<br />=> Use “delta function” which will keep track of changes in the PageRank of all the pages and if the change in PageRank of all the pages is less than the value specified by the user the iterations can be stopped.<br />
Questions</li></li></ul><li>Applications and Extensions<br />A simple model of Search Engine. (Implemented)<br /> The application utilizes: <br />The PageRank calculated by the PageRank Calculator<br />The output generated by a map-reduce module that finds out the number of times a pattern (as per the user’s query) matches in each of the files present in data set.<br />And outputs:<br /> The list of pages which are relevant to the query made in the order of their importance.<br />(DEMO)<br />
Applications and Extensions<br />Other Applications:<br /><ul><li>PageRank-based mechanism to rank knowledge items used in E-Learning.
GeneRank (based on PageRank) ranks the genes analyzed in the microarray to see the relationship between the cell’s function and gene expression.
Can be used to sort the items present in the side menu in various blogs and sites depending on their importance.</li></li></ul><li>References<br />http://infolab.stanford.edu/pub/papers/google.pdf<br /> ( research paper by Brin and Page)<br />http://www.ams.org/featurecolumn/archive/pagerank.html<br />http://en.wikipedia.org/wiki/PageRank<br />http://www.webworkshop.net/pagerank.html#how_is_pagerank_calculated<br />