1. Google’s means to provide better search results Qi-Yuan Gou

2. Considerations Volume of the database How large is the Internet? "The World's Largest Matrix Computation.“ –Cleve Moler, founder of Matlab Source: www.wikipedia.com

3. History Pagerank: What is it? –Larry Page –Sergey Brin –Google Source: www.wikipedia.com

4. Preparation Graph theory –Network analysis Computer science Linear algebra Stochastic process –Markov process Set of possible outcomes/states is finite Probability of n depends only on n-1 The probabilities are constant over time Source: www.york.ac.uk

5. Simple Markov process

6. Complicated Markov Process

7. The Strategy Markov process determines starting matrices Diagonalize Find steady-state vectors Solution gives the overall rankings – PR – to each element

8. The General Case

10. Sample case n=4

11. Source: www.cs.princeton.edu