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?
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?
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.
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
1b. Geben Sie für diesen Graphen die Link- Matrix A mit Teleportation an. Die Teleportationswahrscheinlichkeit sei 25%.
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
= 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
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!
1c. Calculate 5 iterations of PageRank = A telep ( ) = X 0 ( ) = X 1
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 =
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.
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!