Databases Reference
In-Depth Information
A
B
C
D
Figure 5.15: Repeat of example Web graph
Suppose that our topic is represented by the teleport set S ={B, D}. Then
the vector (1−β)e
S
/|S|has 1/10 for its second and fourth components and 0
for the other two components. The reason is that 1−β = 1/5, the size of S is
2, and e
S
has 1 in the components for B and D and 0 in the components for A
and C. Thus, the equation that must be iterated is
2
4
3
5
2
4
3
5
0
2/5
4/5
0
0
1/10
0
1/10
4/15
0
0
2/5
v
′
=
v +
4/15
0
0
2/5
4/15
2/5
0
0
Here are the first few iterations of this equation. We have also started with
the surfers only at the pages in the teleport set. Although the initial distribution
has no effect on the limit, it may help the computation to converge faster.
2
4
3
5
2
4
3
5
2
4
3
5
2
4
3
5
2
4
3
5
0/2
1/2
0/2
1/2
2/10
3/10
2/10
3/10
42/150
41/150
26/150
41/150
62/250
71/250
46/250
71/250
54/210
59/210
38/210
59/210
Notice that because of the concentration of surfers at B and D, these nodes get
a higher PageRank than they did in Example 5.2. In that example, A was the
node of highest PageRank.
2
5.3.3
Using Topic-Sensitive PageRank
In order to integrate topic-sensitive PageRank into a search engine, we must:
1. Decide on the topics for which we shall create specialized PageRank vec-
tors.
2. Pick a teleport set for each of these topics, and use that set to compute
the topic-sensitive PageRank vector for that topic.
