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Page rank
- 2. People Presenting the Algorithm Tahreem Saleem
- 3. If you are searching for something What do you do?? You just GOOGLE it
- 4. But how does a search engine really work?? Early 90’s Text based Ranking systems Problem
- 5. NUST RESULT • www.student_info.pk • www.top10universities.com • www.enginerringuniversity.edu.pk www.nust.edu.pk NUST NUST NUST NUST NUST NUSTNUST NUSTNUST NUST NUST NUST NUST NUST If want to search
- 6. Modern search engines employ methods of ranking the results to provide the "best" results Page Rank algorithm used by the Google search engine Larry Page Sergey Brin Google trademark in 1998
- 7. Idea Of Page Rank The importance of any web page can be judged by looking at the pages that link to it.
- 8. Web Page “A” Web Page “B” MEANS B = Important Hyperlink
- 9. Web Page “C” Web Page “B” MEANS B = Important Hyperlink Web Page “D” Hyperlink
- 10. Web Page “K” Authoritative • www.google.com • www.cnn.com Web Page “B” MEANS ‘K’ transfers authority to ‘B’ Hyperlink
- 11. Web Net as directed graph Nodes represent web pages Edges represent links
- 13. A 0 0 1 1 2 B 1 3 0 0 0 C 1 3 1 2 0 1 2 D 1 3 1 2 0 0 Let us represent it with a matrix “A” A B C D
- 14. The Main formula 𝑃𝑅 𝑝_𝑖 = 1−𝑑 𝑁 + 𝑑 𝑝_𝑗 ∈ 𝑀(𝑝_𝑖) 𝑃𝑅 (𝑝_𝑗) 𝐿(𝑝_𝑗) • p_1, p_2, ..., p_N = pages • M(p_i) = set of pages that link to p_i • L(p_j) = number of outbound link • N = total number of pages • D = Damping factor (0.85)
- 15. Calculations 0 0 1 1 2 1 3 0 0 0 1 3 1 2 0 1 2 1 3 1 2 0 0 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 +0.15* 0.85*
- 16. A 0.037 0.037 0.88 0.46 B 0.32 0.037 0.037 0.037 C 0.32 0.46 0.037 0.46 D 0.32 0.46 0.037 0.037 Which Leads to: A B C D
- 18. Power Iteration Method • Suppose there are N webpages • Initialize: r(0) = [1 𝑵 ,…, 1 𝑵 ]T • Iterate : r(t+1) =M.r(1) • Stop when | r(t+1) - r(0) |<
- 19. Ist step • Initialize: r(0) = 1 4 1 4 1 4 1 4 2nd step rA =0.037* rA +0.037* rB +0.88* rC +0.46* rD rA =0.35* 0.25 +0.35* 0.25 +0.88* 0.25 +0.46* 0.25 rA = 0.35
- 20. 0.25 0.35 0.39 0.34 0.35 0.34 0.25 0.108 0.13 0.14 0.13 0.13 0.25 0.32 0.27 0.28 0.27 0.27 0.25 0.21 0.18 0.20 0.19 0.19 rA rB rC rD T t0 t1 t2 t3 t4 t5
- 21. Rank 1 = A Rank 2 = C Rank 3 = D Rank 4 = B Final Ranks
- 22. Pseudo Code
- 23. Time Complexity Wikipedia Stake Overflow O(n+m) O( log 𝑛 ) n=number of nodes m=number of edges
- 24. Life Before Page Rank
- 25. Life After Page Rank
- 26. Advantages It is a global measure of ranking and it is query independent It is robust against spam. Page Rank algorithm is more feasible in today's scenario since it performs computations at crawl time More Efficient then other ranking algorithm.
- 27. Disadvantages It favor the older pages It is a static algorithm that, because of its cumulative scheme, popular pages tend to stay popular generally PageRank doesn't handle pages with no out edges very well
- 28. References • http://www.math.cornell.edu/~mec/Winter2009/Ra lucaRemus/index.html • http://www.cs.cmu.edu/~elaw/pagerank.pdf • http://www.slideshare.net/maimustafa566/page- rank-algorithm-33212250
- 29. Fin
Editor's Notes
- At first glance, it seems reasonable to imagine that what a search engine does is to keep an index of all web pages, and when a user types in a query search, the engine browses through its index and counts the occurrences of the key words in each web file. The winners are the pages with the highest number of occurrences of the key words. These get displayed back to the user.
- suppose we wanted to find some information about NUST. We type in the word “NUST" and expect that "www.nust.edu.pk" would be the most relevant site to our query. However there may be millions of pages on the web using the world NUST, and www.nust.edu.pk may not be the one that uses it most often. Suppose we decided to write a web site that contains the word “NUST" a billion times and nothing else. Would it then make sense for our web site to be the first one displayed by a search engine?
- Modern search engines employ methods of ranking the results to provide the "best" results first that are more elaborate than just plain text ranking. One of the most known and influential algorithms for computing the relevance of web pages is the Page Rank algorithm used by the Google search engine. It was invented by Larry Page and Sergey Brin while they were graduate students at Stanford, and it became a Google trademark in 1998.
- The idea that Page Rank brought up was that, the importance of any web page can be judged by looking at the pages that link to it. If we create a web page i and include a hyperlink to the web page j, this means that we consider jimportant and relevant for our topic. If there are a lot of pages that link to j, this means that the common belief is that page j is important. If on the other hand, j has only one backlink, but that comes from an authoritative site k, (like www.google.com, www.cnn.com, www.cornell.edu) we say that k transfers its authority to j; in other words, kasserts that j is important. Whether we talk about popularity or authority, we can iteratively assign a rank to each web page, based on the ranks of the pages that point to it.
- If we create a web page i and include a hyperlink to the web page j, this means that we consider jimportant and relevant for our topic. If there are a lot of pages that link to j, this means that the common belief is that page j is important. If on the other hand, j has only one backlink, but that comes from an authoritative site k, (like www.google.com, www.cnn.com, www.cornell.edu) we say that k transfers its authority to j; in other words, kasserts that j is important. Whether we talk about popularity or authority, we can iteratively assign a rank to each web page, based on the ranks of the pages that point to it.
- If we create a web page i and include a hyperlink to the web page j, this means that we consider jimportant and relevant for our topic. If there are a lot of pages that link to j, this means that the common belief is that page j is important. If on the other hand, j has only one backlink, but that comes from an authoritative site k, (like www.google.com, www.cnn.com, www.cornell.edu) we say that k transfers its authority to j; in other words, kasserts that j is important. Whether we talk about popularity or authority, we can iteratively assign a rank to each web page, based on the ranks of the pages that point to it.
- If we create a web page i and include a hyperlink to the web page j, this means that we consider jimportant and relevant for our topic. If there are a lot of pages that link to j, this means that the common belief is that page j is important. If on the other hand, j has only one backlink, but that comes from an authoritative site k, (like www.google.com, www.cnn.com, www.cornell.edu) we say that k transfers its authority to j; in other words, kasserts that j is important. Whether we talk about popularity or authority, we can iteratively assign a rank to each web page, based on the ranks of the pages that point to it.
- we begin by picturing the Web net as a directed graph, with nodes represented by web pages and edges represented by the links between them.
- For the purpose of computing their page rank, we ignore any navigational links such as back, next buttons, as we only care about the connections between different web sites. For instance, Page1 links to all of the other pages, so node 1 in the graph will have outgoing edges to all of the other nodes. Page3 has only one link, to Page 1, therefore node 3 will have one outgoing edge to node 1. After analyzing each web page, we get the following graph: In our model, each page should transfer evenly its importance to the pages that it links to. Node 1 has 3 outgoing edges, so it will pass on of its importance to each of the other 3 nodes. Node 3 has only one outgoing edge, so it will pass on all of its importance to node 1. In general, if a node has k outgoing edges, it will pass on of its importance to each of the nodes that it links to. Let us better visualize the process by assigning weights to each edge.
- : PR(p_i) = \frac{1-d}{N} + d \sum_{p_j \in M(p_i)} \frac{PR (p_j)}{L(p_j)} where p_1, p_2, ..., p_N are the pages under consideration, M(p_i) is the set of pages that link to p_i, L(p_j) is the number of outbound links on page p_j, and N is the total number of pages.
- O(n+m) ( n - number of nodes, m - number of arcs/edges)
- http://en.wikipedia.org/wiki/PageRank http://www.math.cornell.edu/~mec/Winter2009/RalucaRemus/index.html http://www.cs.cmu.edu/~elaw/pagerank.pdf http://www.slideshare.net/maimustafa566/page-rank-algorithm-33212250