Mathematics at Google
Brief history
• Started in 1996 as the research project
‘Backrub’ by the then PhD student Larry Page
• Sergey Brin joined in
• Became incorporated in 1998
• Began selling advertisement in 2000
• Became public in 2004
– Initial raise $2,718,281,828 (e * 10 ^ 9)
– Implied value of 23 billion
The 25,000,000,000 vector
• Represent the web as a huge directed graph
• Constantly traversed by a “random web surfer”
• Forward and backlinks
• The importance of each page is based on
importance of the pages linking to it
• Importance of a page
• Transition matrix
• Stohastic matrix
– All entries are non negative
– The sum of all entries in a column is 1 (unless the
node corresponding to that column has no links)
Dangling nodes
• Nodes with no forward links
Dangling nodes (continued)
• If A is the matrix whose entries are all zero
except for the columns corresponding to
dangling nodes, in which each entry is 1/n,
then S = H + A.
Final Matrix
• Google Matrix
• α – damping factor, usually 0.85
Other examples
• Google maps – graph of all cities.
- Selected route is the shortest path between the
nodes
- YouTube rankings
- Ad serving
- Selection algorithm
- Various areas of research
Forecasting
• Simulation of the ad server
• Sampling of data
• Ad selection based on satisfaction index of the
ad
Machine Learning
• Marriage between statistics and computer
science
• Adaptive models for predicting and classifying
data
regression analysis, neural networks, support
vector machines
Math in management
Chief Economist of Google is Hal Varian
- professor in University of Berkeley specializing
in microeconomics and information
technology
- Employee ratings
- Resource allocations