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ITI 111 Spring 2011 Practice final Exam
There are 4 web pages in a small internet. Call them A,B,C,D
Each has a representation using a basis of terms:
Page
People
love
hate
war
2

P
A
3
2
1
0
14
B
0
1
2
4
21
C
1
0
1
1
3
D
2
4
0
0
20
Q
1
1
0
0
2
A user has entered the query Q: “families people love”.
1.
In the space provided in the table above, write the vector for Q in the same basis.
2.
Rank the 4 web pages (p=A,B,C,D) using the inner product <Qp>. Let’s call this
ranking system
R1
.
Answer:
Rank 1:
D (6)
Rank 2:
A (5)
Rank 3:
C (1 and shorter term vector, so ranks above B)
Rank 4:
B (1)
3.
Now rank them using the cosine of the angle between the page and the query.
Let’s call this ranking system
R2
.
D (18.4°)
A (19.1°)
C (65.9°)
B (81.1°)
4.
Now compute the modified Kendalls’ Tau similarity between these two different
ways of ranking,
and
.
Total number of pairs
TP
=
4
2
=
6
Pairs out of order
OO
=
0
Tau =
1
OO
TP
=
1
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B
C
D
5.
These pages are linked in a tiny internet
5: Write the adjacency matrix of this digraph
A=
[
±
²
±
±
±
²
±
]
6.
Write the message matrix
T
MA
M
=
[
±
±
²
±
±
²
±
]
7.
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This note was uploaded on 02/20/2012 for the course 790 373 taught by Professor Boros during the Fall '09 term at Rutgers.
 Fall '09
 Boros

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