Talk:PageRank

message: 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)
thread_title:  Unnecessary assumption in derivation of power method? 

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thread_title:  External links modified 

message: 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)
thread_title:  Minor error in "Damping Factor" 

message: 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)
replies: text: 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)
thread_title:  Damping factor for biological data 

message: 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)
thread_title:  Variables lack clear names 

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

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thread_title:  "[[:Supplemental Result]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]