Group: Nathan Taylor

Title:  Eigen See What's Relevant: Explaining the Linear Algebra in the Google PageRank Algorithm

Abstract: To prioritize and provide information concerning the relevance of any given web page, Google calculates a value called a Page Rank for each web page in its network. The algorithm to calculate the Page rank is based 
off of a stochastic matrix and eigenvectors. This project will explore the 
principles behind the Google Page Rank and the use of linear algebra in performing its calculations.



Outline:

Page Relevance: Websites cannot be ranked in relevance simply on the number
 of times a word in a search appears in a website. Google developed a system that would rank websites by the importance of other websites that linked to them.


Creating a Markov Matrix: Each week, Google checks each web page in its network to count the number of links each webpage has to each other page. A probability matrix is created based off of the number of links each web page has and to which pages it links.


Eigenvectors: If there are N pages listed in Google's network, then the value of the relevance of each page is computed as 1/N and placed in a vector in dimension R^N. A Markov chain is created using this vector and the matrix described in the last section and continues iterating until the eigenvector corresponding to 1 is produced. This vector contains the PageRank values of all the pages in Google's network, and works as a main factor in the order in which pages are displayed in a Google search.