Google’s means to provide better search results

Qi-Yuan Gou

Considerations

• Volume of the database

• How large is the Internet?

• "The World's Largest Matrix Computation.“– Cleve Moler, founder

of MatlabSource: www.wikipedia.com

Source: www.wikipedia.com

History

• Pagerank: What is it?

– Larry Page

– Sergey Brin

– GoogleSource: www.wikipedia.com

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 timeSource: www.york.ac.uk

Simple Markov process

Complicated Markov Process

The Strategy

• Markov process determines starting matrices

• Diagonalize

• Find steady-state vectors

• Solution gives the overall rankings – PR – to each

element

The General Case

Sample case n=4

Source: www.cs.princeton.edu