User Tools

Site Tools


gibson:teaching:spring-2018:math445:lab6

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
gibson:teaching:spring-2018:math445:lab6 [2018/03/21 11:29]
gibson
gibson:teaching:spring-2018:math445:lab6 [2018/03/21 11:41] (current)
gibson
Line 41: Line 41:
 where $[1]$ is an $M \times M$ matrix of ones. Rumor has it that Google uses $\alpha = 0.15$, so use that value and calculate $B$.  where $[1]$ is an $M \times M$ matrix of ones. Rumor has it that Google uses $\alpha = 0.15$, so use that value and calculate $B$. 
  
-**(d)** Double-check that the sum of each column of $B$ is 1. Again, be clever and get Matlab to do the work, rather than listing out the sums of all the columns and verifying manually that each of the 100 numbers is 1! +**(d)** Double-check that the sum of each column of $B$ is 1. Again, be clever and get Matlab to do the work, rather than listing out the sums of all the columns and verifying manually that each of the $M$ numbers is 1! 
  
 **(e)** Let’s assume that all websurfers start at the first webpage, ''​x=zeros(M,​1);​ x(1)=1;''​. If we iteratively apply ''​B''​ to ''​x''​ many times (say 40 times), the resulting vector will give the probability that we end up on a particular website and after a long session of random web surfing. We can do this with a for-loop **(e)** Let’s assume that all websurfers start at the first webpage, ''​x=zeros(M,​1);​ x(1)=1;''​. If we iteratively apply ''​B''​ to ''​x''​ many times (say 40 times), the resulting vector will give the probability that we end up on a particular website and after a long session of random web surfing. We can do this with a for-loop
Line 56: Line 56:
  
 **(f)** ​ If you are interested: Our calculation involved two free parameters: the probability $\alpha$ of jumping to an entirely random page in the network, and $N$, the number that specifies the length of our long session of random web surfing. How robust is the page rank algorithm with respect to these two parameters? If you change $\alpha$ to 0.1 or 0.05, do the top 10 pages change? **(f)** ​ If you are interested: Our calculation involved two free parameters: the probability $\alpha$ of jumping to an entirely random page in the network, and $N$, the number that specifies the length of our long session of random web surfing. How robust is the page rank algorithm with respect to these two parameters? If you change $\alpha$ to 0.1 or 0.05, do the top 10 pages change?
-How about if you change ​''​M'' ​to 100 or 1,000?+How about if you change ​$Mto 64128, 256, 512, or 1024(some of these larger values might take a really long time). ​
  
 ---- ----
gibson/teaching/spring-2018/math445/lab6.txt · Last modified: 2018/03/21 11:41 by gibson