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 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 Both sides previous revision Previous revision 2018/03/21 11:41 gibson 2018/03/21 11:29 gibson 2018/03/21 09:17 gibson 2018/03/21 09:16 gibson 2018/03/06 06:59 gibson 2018/03/06 06:48 gibson 2018/03/06 06:46 gibson created 2018/03/21 11:41 gibson 2018/03/21 11:29 gibson 2018/03/21 09:17 gibson 2018/03/21 09:16 gibson 2018/03/06 06:59 gibson 2018/03/06 06:48 gibson 2018/03/06 06:46 gibson created 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 ​$M$ to 64, 128, 256, 512, or 1024? (some of these larger values might take a really long time). ​ ---- ----