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Google’s PageRank algorithm powered by linear algebra Andrew Dynneson Fall 2010 Abstract Google’s PageRank algorithm ranks the importance of internet pages using a number of factors to be discused, such as backlinking, which can be computed using eigenvectors and stochastic matrices. However, due to the overwhelmingly large number of web-pages available on the internet, another method must be employed which will be a modified power method, which accurately approximates the ranking. 1. Introduction: the basic algorithm Up until this semester in Linear Algebra, I had mistakenly assumed that Google ranked pages in order of importance based on how much money the host URL was willing to pay for that ranking. To take a line from Schindler’s List, “Call it gratuity.” Upon professing my ignorance, I discovered that the actual proceedure for determining which listing shows up on the first result pages is actually an incredibly in-depth proceedure using Semantic Analysis and Linear-Algebra. This paper gives an explanation of one aspect of Google’s ranking, known as the “Page-Rank Algorithm.” The complete nature of how PageRank works is not entirely known, nor is PageRank in the public domain. Most of the articles that discuss the algorithm indicate that it works by Markov chains. However, the algorithm runs into trouble when there are dangling nodes [2] (pages that do not link to other pages). In other words, there is considerable mystery surrounding the workings of Google’s algorithm. For information on the workings of the original algorithm, see [5]. The authors in [5] also provide us with some colorful verbiage, which accentuates the neccessity of PagRank quite nicely: The average web page quality experienced by a user is higher than the quality of the average web page. This is because the simplicity of creating and publishing web pages results in a large fraction of low quality pages that users are unlikely to read. PageRank works by forming a de facto democracy of links, where each link to another page acts as a vote. These votes are weighted according to importance of the website placing the vote, and are scaled according to how many votes a website casts [1,2,3]. Beginning with a crude example, and it will be shown how the majorant with respect to raw votes is usurped once weighting is applied. Consider this elementary model of an internet consisting of only four 1PDF Image | Google PageRank algorithm powered by linear algebra
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