Talk:PageRank

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Removed[edit]

Google uses an automated web spider called Googlebot to actually count links and gather other information on web pages.

It is by no means clear that the counting can be said to be done by Googlebot, and it is not intuitively a spidering operation, more likely a feature of the database to which the spidering software stores its flies. Therefore this needs a citation to be in the article. Clearly what parts of the Google infrastructure are called "Googlebot" is up to Google, however if it extends too far, the description needs to be changed. All the best: Rich Farmbrough, 13:25, 11 August 2014 (UTC).

Unnecessary assumption in derivation of power method?[edit]

In the power method section, the first step of the derivation is :

If the matrix \mathcal{M} is a transition probability, i.e., column-stochastic with no columns consisting of just zeros and \mathbf{R} is a probability distribution (i.e., |\mathbf{R}|=1, \mathbf{E}\mathbf{R}=\mathbf{1} where \mathbf{E} is matrix of all ones), Eq. (**) is equivalent to 

   \mathbf{R} = \left( d \mathcal{M} + \frac{1-d}{N} \mathbf{E} \right)\mathbf{R} =: \widehat{ \mathcal{M}} \mathbf{R}.       (***)

And so on...

My Question: Is it necessary that \mathcal{M} has this particular property for this step of the derivation to hold? It seems that only the property that R is a probability distribution is required. — Preceding unsigned comment added by Mtjoul (talk • contribs) 22:41, 21 December 2014 (UTC)[reply]

External links modified[edit]

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  • What does the link: Our products and services by Google have to do with PageRank? I followed the link but could not find PageRank. If it is somewhere at that URL, then the link should be refined. 5.34.22.174 (talk) 04:41, 5 January 2018 (UTC)[reply]

Minor error in "Damping Factor"[edit]

In "Damping Factor", after the two formulas, it states, "The difference between them is that the PageRank values in the first formula sum to one, while in the second formula each PageRank is multiplied by N and the sum becomes N." However (unless I'm blind), from the first equation to the second, only the first part has been multiplied by N. (Otherwise you'd have 1 - d + Nd(stuff).) With the second equation given as-is, the sum of page ranks is rather trickier than "N". Given that the equation is already acknowledged to be wrong, it's probably not urgent, but hey. — Preceding unsigned comment added by 98.102.161.228 (talk) 17:37, 22 August 2016 (UTC) The parameter of this code is good to be used in many problems..hoursguru.com[reply]

Damping factor for biological data[edit]

The article mentions 0.31 as the optimal value for d, however nowhere in the cited paper can I directly find 0.31. I can find a reference to an epsilon of 0.3 in Appendix 1.1, but I am not yet convinced this is equivalent to the damping factor d. Can someone clarify? --José Devezas (talk) 08:19, 19 December 2018 (UTC)[reply]

I also wonder whether the statement even makes sense. How can there be a single damping factor for all "biological data"? What application are we talking about? What is being modelled? I will remove the statement. If someone feels it adds value or explanatory power to the article, perhaps they can clarify it. GBMorris (talk) 13:25, 9 March 2020 (UTC)[reply]

I agree with the points raised by both of you and consider the removal of the statement a good decision. BernardoSulzbach (talk) 20:50, 9 March 2020 (UTC)[reply]

Examples are Wrong[edit]

  • It's not clear what does the value 0.5 represents
  • The sum(i, M_i,j) is never 1
  • I think columns/rows have been messed up. Comments mention that M_i,j represents link from j to i, but if you run a clear example, e.g, the following:

everything links to A which means A is an important page, and A links to C, thus C is important as well. 

   M = np.array([
       [1, 1, 1],  # * -> A
       [0, 0, 0], 
       [1, 0, 0]   # A -> C
   ])
  print(pagerank(M, 0.001, 0.85)) 
  array([[0.61536926],  
         [0.28131799],
         [0.10331275]])

B should be last but its second. Am I missing something?

I'm not sure which version of the algorithm this edit was referring to, but I've been working with it and it works; in this case, [1, 1, 1] should be impossible because A cannot link to itself. A links to C would be [0, 0, 1] on the A row if [A, B, C], and A links to both B and C would be [0, 1, 1]. I'm also not sure what the call to `pagerank(..., 0.001, ...)` is meant to do, since `0.001` doesn't make sense as the number of iterations (I'm guessing it would iterate once).
--D.g.lab. (talk) 16:31, 10 April 2021 (UTC)[reply]
I'm also not sure what was meant by the sum of (i, M_i, j) is 1 since half those variable names don't exist in the code. It could be said that the sum of every column in the matrix is 1?
The sum of the result vector, called v in the code, should also be approximately 1, I believe, since it contains percentages.
--D.g.lab. (talk) 16:39, 10 April 2021 (UTC)[reply]

Variables lack clear names[edit]

It's already difficult enough to understand as it is, why not clarify the variable names and add comments, as in any good code? For example: 

   def pagerank(matrix, num_iterations: int = 100, damping: float = 0.85):
       size = matrix.shape[1]
       res_vector = [1/size] * size
       M_hat = (damping * matrix + (1 - damping) / size)
       for i in range(num_iterations):
           res_vector = M_hat @ res_vector # matrix multiplication
       return res_vector

Also, notice the lines in the article: 

   v = np.random.rand(N, 1)
   v = v / np.linalg.norm(v, 1)

these insert random numbers in the multiplication vector. However, as far as I understand, this vector is supposed to start initially as `1/number_of_pages` (1/size) for each of its elements, which could be re-written 

   v = [1/N] * N

or, using the new varible names, 

   res_vector = [1/size] * size

According to this video on YouTube: Linear Algebra – Introduction to PageRank (4:21 timestamp).

I'm unsure why this was like this, so I'm not editing the page; however, if someone can confirm, the initial method seems "way too complicated" and there's no explanation for it. --D.g.lab. (talk) 16:31, 10 April 2021 (UTC)[reply]

site:example.com[edit]

😐site:example.com 2A00:F41:4828:36B6:0:4B:5D7E:4801 (talk) 23:52, 24 February 2022 (UTC)[reply]

reference 25 is old[edit]

the article states:'PageRank continues to be the basis of googles....'[25] reference 25 is over 10y old so it does not prove anything. 213.247.64.239 (talk) 14:32, 18 January 2023 (UTC)[reply]

@213.247.64.239
actual text from the article:
'While just one of many factors that determine the ranking of Google search results, PageRank continues to provide the basis for all of Google's web-search tools.' 213.247.64.239 (talk) 14:33, 18 January 2023 (UTC)[reply]
Google doesn't disclose the details of its ranking systems, but they have affirmed that PageRank remains one of the many signals they use. While there might be a more recent reference, it wouldn't be very precise. They don't disclose those kinds of details. While this article could use some clean up, it's not inaccurate in saying that Google still uses the algorithm. Michael Martinez (talk) 15:01, 18 January 2023 (UTC)[reply]
Google recently added new documentation that confirms PageRank is still used in their ranking systems although it has evolved since the original paper (in unspecified ways).Michael Martinez (talk) 13:01, 25 April 2023 (UTC)[reply]
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