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 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) = 0.75 4.Add constant (c/N*e) 5.DOUBLE CHECK!!! 1b. Link Matrix with Teleportation

7 0.05 0.425 0.05 0.425 0.051 0.425 0.05 0.05 0.425 0.051 0.05 0.05 0.05 0.8 0.05 = A telep (= 1 ) 0.05 0.8 0.05 0.05 0.051 0.2 0.2 0.2 0.2 0.21 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 0.05 0.425 0.05 0.425 0.05 0.425 0.05 0.05 0.425 0.05 0.05 0.05 0.05 0.8 0.05 = A telep 0.05 0.8 0.05 0.05 0.05 0.2 0.2 0.2 0.2 0.2 (0.2 0.2 0.2 0.2 0.2) = X 0 (0.155 0.305 0.08 0.38 0.08 ) = X 1

10 1c. Calculate 5 iterations of PageRank (continued) (0.2 0.2 0.2 0.2 0.2) = X 0 (0.155 0.305 0.08 0.38 0.08 ) = X 1 (0.17638 0.40513 0.062 0.2945 0.062) = X 2 (0.21122 0.34639 0.0593 0.32387 0.0593) = X 3 (0.18880 0.38101 0.0589 0.31248 0.0589 ) = X 4 X 1 = 1 X 2 = 1.00001 X 3 = 1.00008 X 4 = 1.00009

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!