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PageRank 1.What does the graph represent? 2.Describe PageRank. 3.What does PageRank measure in a graph? 4.Which role does PageRank play in IR?

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Präsentation zum Thema: "PageRank 1.What does the graph represent? 2.Describe PageRank. 3.What does PageRank measure in a graph? 4.Which role does PageRank play in IR?"—  Präsentation transkript:

1 PageRank 1.What does the graph represent? 2.Describe PageRank. 3.What does PageRank measure in a graph? 4.Which role does PageRank play in IR?

2 PageRank 1.What does the graph represent? 2.Describe PageRank. 3.What does PageRank measure in a graph? 4.Which role does PageRank play in IR?

3 1a. Ordnen Sie die Knoten in dem Graphen basierend auf deren voraussichtlichen PageRank Werte (dafür ist keine PageRank Berechnung erforderlich!). Begründen Sie die von Ihnen erstellte Reihenfolge.

4 1a. Rank nodes No inlinks – E, C bottom ranked One inlink – A middle rank Two or more inlinks – AND links to each other – B,D top ranked

5 1b. Geben Sie für diesen Graphen die Link- Matrix A mit Teleportation an. Die Teleportationswahrscheinlichkeit sei 25%.

6 1.Create Link Matrix 2.Normalize Link Matrix 3.Multiply with (1-c) = Add constant (c/N*e) 5.DOUBLE CHECK!!! 1b. Link Matrix with Teleportation

7 = A telep (= 1 ) Check that the sum of each row = 1 Note that the diagonal elements are 0.05 and 0.2 because we only reach our selves by teleportation! A telep

8 1c. Gegeben sei die PageRank-Formel: e sei 1. Im x sind die Zufallssurfer gleichverteilt. Berechnen Sie für den gegebenen Graphen den Vektor x für die ersten 5 Iterationen der PageRank-Formel (k = 0..4). Geben sie die Werte nicht-normalisiert und auf fünf Nachkommastellen genau an!

9 1c. Calculate 5 iterations of PageRank = A telep ( ) = X 0 ( ) = X 1

10 1c. Calculate 5 iterations of PageRank (continued) ( ) = X 0 ( ) = X 1 ( ) = X 2 ( ) = X 3 ( ) = X 4 X 1 = 1 X 2 = X 3 = X 4 =

11 Extras One can consider the transportation as an extra dummy-node which the surfer chooses with probability c. The vector can be seen as a personalization vector. How? – Give larger probabilities to nodes that the random surfer is more likely to visit. E.g., For a German surfer, increase probabilities for German web pages and lower probabilities for all overs.

12 Tip! In A the rows are the outlinks of a node and the columns are the inlinks! Double check with the graph that it was right! After normalization: rows in A and A telep sum to 1. After every iteration, check that the PageRank values sum to 1!


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