Google-ov PageRank Algoritam
description
Transcript of Google-ov PageRank Algoritam
Aleksandar MilinkovićElektrotehnički fakultet
Google-ov PageRank Algoritam
Aleksandar MilinkovićElektrotehnički fakultet u Beogradu
Aleksandar MilinkovićElektrotehnički fakultet
2/16
Pretraživanje na webu se razlikuje od klasičnog
Web je:Ogroman (oko 40 milijardi stranica)
Dinamičan
Samoorganizujući
Hiperlinkovan
Uvod
Ovim nije obuhvaćen tzv. duboki web
Aleksandar MilinkovićElektrotehnički fakultet
3/16
Principi rada web pretraživača
WWW
Crawler modul
Repozitorijum web stranica
Modul za indeksiranje
Modul za upite
Modul za rangiranje
korisnik
Indeks sadržaja
Indeks specijalne nameme
Moduli nezavisni od upita
Indeks strukture
upit rezultat
Aleksandar MilinkovićElektrotehnički fakultet
4/16
PageRank Algoritam – model 1
001000
000000
010010
000010
000001
001110 A B C D E F
A B
C
D
E
F
1
1
1
1
1
1
e
1
0
2
1
1
3
eM ?
Zar ne bi trebalo da čvor B ima veći rang od čvora D
Aleksandar MilinkovićElektrotehnički fakultet
5/16
PageRank Algoritam – model 2
e
0 kk M 1
11
1
0
2
1
1
3
1
1
1
1
1
1
001000
000000
010010
000010
000001
001110
eM 22
2
0
1
1
3
4
1
0
2
1
1
3
001000
000000
010010
000010
000001
001110
eM 33
1
0
3
3
4
5
2
0
1
1
3
4
001000
000000
010010
000010
000001
001110
eM 44
3
0
4
4
5
10
1
0
3
3
4
5
001000
000000
010010
000010
000001
001110
eM 55
4
0
5
5
10
13
3
0
4
4
5
10
001000
000000
010010
000010
000001
001110
eM 66
5
0
10
10
13
20
4
0
5
5
10
13
001000
000000
010010
000010
000001
001110
πeM
77
10
0
13
13
20
33
5
0
10
10
13
20
001000
000000
010010
000010
000001
001110
πeM
88
13
0
20
20
33
46
10
0
13
13
20
33
001000
000000
010010
000010
000001
001110
πeM
?Kada prestati sa iteriranjem?
Rangovi stranica postaju veliki
Aleksandar MilinkovićElektrotehnički fakultet
6/16
Skaliranje kolona tako da ukupan zbir bude 1
PageRank Algoritam – model 3
0 1 1 1 0 0
1 0 0 0 0 0
0 1 0 0 0 0
0 1 0 0 1 0
0 0 0 0 0 0
0 0 0 1 0 0
M
1 13 2
13
13
12
0 1 0 0
1 0 0 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0 0
0 0 0 0 0
H
0
1en
1k kH
Aleksandar MilinkovićElektrotehnički fakultet
7/16
PageRank Algoritam – model 30
1 1 13 2 6
16
1 13 60
0 1 13 6
16
1 12 6
0 1 0 0 0.17
1 0 0 0 0 0 0.17
0 0 0 0 0 0.171
0 0 0 1 0 0.17
0 0 0 0 0 0 0.17
0 0 0 0 0 0.17
H en
Rangovi svih stranica konvergiraju ka 0
F je viseći (dangling) čvor
?1
1 1 13 2 6
16
1 13 61
1 1 13 6
16
1 12 6
0 1 0 0 0.31
1 0 0 0 0 0 0.17
0 0 0 0 0 0.061
0 0 0 1 0 0.22
0 0 0 0 0 0 0.00
0 0 0 0 0 0.08
H en
21 1 1
3 2 6
16
1 13 62
2 1 13 6
16
1 12 6
0 1 0 0 0.22
1 0 0 0 0 0 0.31
0 0 0 0 0 0.061
0 0 0 1 0 0.06
0 0 0 0 0 0 0.00
0 0 0 0 0 0.11
H en
31 1 1
3 2 6
16
1 13 63
3 1 13 6
16
1 12 6
0 1 0 0 0.19
1 0 0 0 0 0 0.22
0 0 0 0 0 0.101
0 0 0 1 0 0.10
0 0 0 0 0 0 0.00
0 0 0 0 0 0.03
H en
41 1 1
3 2 6
16
1 13 64
4 1 13 6
16
1 12 6
0 1 0 0 0.23
1 0 0 0 0 0 0.19
0 0 0 0 0 0.071
0 0 0 1 0 0.07
0 0 0 0 0 0 0.00
0 0 0 0 0 0.05
H en
51 1 1
3 2 6
16
1 13 65
5 1 13 6
16
1 12 6
0 1 0 0 0.17
1 0 0 0 0 0 0.23
0 0 0 0 0 0.061
0 0 0 1 0 0.06
0 0 0 0 0 0 0.00
0 0 0 0 0 0.04
H en
61 1 1
3 2 6
16
1 13 66
6 1 13 6
16
1 12 6
0 1 0 0 0.17
1 0 0 0 0 0 0.17
0 0 0 0 0 0.081
0 0 0 1 0 0.08
0 0 0 0 0 0 0.00
0 0 0 0 0 0.03
H en
71 1 1
3 2 6
16
1 13 67
7 1 13 6
16
1 12 6
0 1 0 0 0.17
1 0 0 0 0 0 0.17
0 0 0 0 0 0.061
0 0 0 1 0 0.06
0 0 0 0 0 0 0.00
0 0 0 0 0 0.04
H en
81 1 1
3 2 6
16
1 13 68
8 1 13 6
16
1 12 6
0 1 0 0 0.14
1 0 0 0 0 0 0.17
0 0 0 0 0 0.061
0 0 0 1 0 0.06
0 0 0 0 0 0 0.00
0 0 0 0 0 0.03
H en
81 1 1
3 2 6
16
1 13 68
8 1 13 6
16
1 12 6
0 1 0 0 0.14
1 0 0 0 0 0 0.17
0 0 0 0 0 0.061
0 0 0 1 0 0.06
0 0 0 0 0 0 0.00
0 0 0 0 0 0.03
H en
91 1 1
3 2 6
16
1 13 69
9 1 13 6
16
1 12 6
0 1 0 0 0.14
1 0 0 0 0 0 0.14
0 0 0 0 0 0.061
0 0 0 1 0 0.06
0 0 0 0 0 0 0.00
0 0 0 0 0 0.03
H en
101 1 1
3 2 6
16
1 13 610
10 1 13 6
16
1 12 6
0 1 0 0 0.13
1 0 0 0 0 0 0.14
0 0 0 0 0 0.051
0 0 0 1 0 0.05
0 0 0 0 0 0 0.00
0 0 0 0 0 0.03
H en
111 1 1
3 2 6
16
1 13 611
11 1 13 6
16
1 12 6
0 1 0 0 0.12
1 0 0 0 0 0 0.14
0 0 0 0 0 0.051
0 0 0 1 0 0.05
0 0 0 0 0 0 0.00
0 0 0 0 0 0.02
H en
121 1 1
3 2 6
16
1 13 612
12 1 13 6
16
1 12 6
0 1 0 0 0.11
1 0 0 0 0 0 0.12
0 0 0 0 0 0.041
0 0 0 1 0 0.04
0 0 0 0 0 0 0.00
0 0 0 0 0 0.02
H en
131 1 1
3 2 6
16
1 13 613
13 1 13 6
16
1 12 6
0 1 0 0 0.11
1 0 0 0 0 0 0.11
0 0 0 0 0 0.041
0 0 0 1 0 0.04
0 0 0 0 0 0 0.00
0 0 0 0 0 0.02
H en
141 1 1
3 2 6
16
1 13 614
14 1 13 6
16
1 12 6
0 1 0 0 0.10
1 0 0 0 0 0 0.11
0 0 0 0 0 0.041
0 0 0 1 0 0.04
0 0 0 0 0 0 0.00
0 0 0 0 0 0.02
H en
151 1 1
3 2 6
16
1 13 615
15 1 13 6
16
1 12 6
0 1 0 0 0.09
1 0 0 0 0 0 0.10
0 0 0 0 0 0.041
0 0 0 1 0 0.04
0 0 0 0 0 0 0.00
0 0 0 0 0 0.02
H en
161 1 1
3 2 6
16
1 13 616
16 1 13 6
16
1 12 6
0 1 0 0 0.09
1 0 0 0 0 0 0.09
0 0 0 0 0 0.031
0 0 0 1 0 0.03
0 0 0 0 0 0 0.00
0 0 0 0 0 0.02
H en
171 1 1
3 2 6
16
1 13 617
17 1 13 6
16
1 12 6
0 1 0 0 0.08
1 0 0 0 0 0 0.09
0 0 0 0 0 0.031
0 0 0 1 0 0.03
0 0 0 0 0 0 0.00
0 0 0 0 0 0.02
H en
181 1 1
3 2 6
16
1 13 618
18 1 13 6
16
1 12 6
0 1 0 0 0.06
1 0 0 0 0 0 0.08
0 0 0 0 0 0.031
0 0 0 1 0 0.03
0 0 0 0 0 0 0.00
0 0 0 0 0 0.02
H en
191 1 1
3 2 6
16
1 13 619
19 1 13 6
16
1 12 6
0 1 0 0 0.06
1 0 0 0 0 0 0.06
0 0 0 0 0 0.031
0 0 0 1 0 0.03
0 0 0 0 0 0 0.00
0 0 0 0 0 0.01
H en
201 1 1
3 2 6
16
1 13 620
20 1 13 6
16
1 12 6
0 1 0 0 0.05
1 0 0 0 0 0 0.06
0 0 0 0 0 0.021
0 0 0 1 0 0.02
0 0 0 0 0 0 0.00
0 0 0 0 0 0.01
H en
211 1 1
3 2 6
16
1 13 621
21 1 13 6
16
1 12 6
0 1 0 0 0.05
1 0 0 0 0 0 0.05
0 0 0 0 0 0.021
0 0 0 1 0 0.02
0 0 0 0 0 0 0.00
0 0 0 0 0 0.01
H en
Aleksandar MilinkovićElektrotehnički fakultet
8/16
F ne preporučuje nijednu stranicu
Rešenje – F preporučuje sve stranice podjednako
PageRank Algoritam – model 4
1 1 13 2 6
16
1 13 6
1 13 6
16
1 12 6
0 1 0
1 0 0 0 0
0 0 0 0
0 0 0 1
0 0 0 0 0
0 0 0 0
S
1 13 2
13
13
12
0 1 0 0
1 0 0 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0 0
0 0 0 0 0
H
0
1en
1k kS 1 TS H ea
n
0 0 0 0 0 1Ta
Aleksandar MilinkovićElektrotehnički fakultet
9/16
PageRank Algoritam – model 40
1 1 1 13 2 6 6
1 16 6
1 1 13 6 60
0 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.17
1 0 0 0 0 0.17
0 0 0 0 0.171
0 0 0 1 0.17
0 0 0 0 0 0.17
0 0 0 0 0.17
S en
11 1 1 1
3 2 6 6
1 16 6
1 1 13 6 61
1 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.33
1 0 0 0 0 0.19
0 0 0 0 0.081
0 0 0 1 0.25
0 0 0 0 0 0.03
0 0 0 0 0.11
S en
21 1 1 1
3 2 6 6
1 16 6
1 1 13 6 62
2 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.29
1 0 0 0 0 0.35
0 0 0 0 0.081
0 0 0 1 0.11
0 0 0 0 0 0.02
0 0 0 0 0.14
S en
31 1 1 1
3 2 6 6
1 16 6
1 1 13 6 63
3 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.28
1 0 0 0 0 0.32
0 0 0 0 0.141
0 0 0 1 0.16
0 0 0 0 0 0.02
0 0 0 0 0.08
S en
41 1 1 1
3 2 6 6
1 16 6
1 1 13 6 64
4 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.34
1 0 0 0 0 0.29
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.09
S en
51 1 1 1
3 2 6 6
1 16 6
1 1 13 6 65
5 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.30
1 0 0 0 0 0.36
0 0 0 0 0.111
0 0 0 1 0.13
0 0 0 0 0 0.02
0 0 0 0 0.09
S en
61 1 1 1
3 2 6 6
1 16 6
1 1 13 6 66
6 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.31
1 0 0 0 0 0.32
0 0 0 0 0.131
0 0 0 1 0.15
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
71 1 1 1
3 2 6 6
1 16 6
1 1 13 6 67
7 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.33
1 0 0 0 0 0.32
0 0 0 0 0.121
0 0 0 1 0.13
0 0 0 0 0 0.01
0 0 0 0 0.09
S en
81 1 1 1
3 2 6 6
1 16 6
1 1 13 6 68
8 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.31
1 0 0 0 0 0.34
0 0 0 0 0.121
0 0 0 1 0.13
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
91 1 1 1
3 2 6 6
1 16 6
1 1 13 6 69
9 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.32
0 0 0 0 0.131
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
101 1 1 1
3 2 6 6
1 16 6
1 1 13 6 610
10 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.13
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
111 1 1 1
3 2 6 6
1 16 6
1 1 13 6 611
11 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.31
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
121 1 1 1
3 2 6 6
1 16 6
1 1 13 6 612
12 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.32
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
131 1 1 1
3 2 6 6
1 16 6
1 1 13 6 613
13 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
141 1 1 1
3 2 6 6
1 16 6
1 1 13 6 614
14 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.31
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
151 1 1 1
3 2 6 6
1 16 6
1 1 13 6 615
15 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
161 1 1 1
3 2 6 6
1 16 6
1 1 13 6 616
16 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.31
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
171 1 1 1
3 2 6 6
1 16 6
1 1 13 6 617
17 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.31
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
181 1 1 1
3 2 6 6
1 16 6
1 1 13 6 618
18 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
191 1 1 1
3 2 6 6
1 16 6
1 1 13 6 619
19 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.31
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
201 1 1 1
3 2 6 6
1 16 6
1 1 13 6 620
20 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
211 1 1 1
3 2 6 6
1 16 6
1 1 13 6 621
21 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
221 1 1 1
3 2 6 6
1 16 6
1 1 13 6 622
22 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.31
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
231 1 1 1
3 2 6 6
1 16 6
1 1 13 6 623
23 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
241 1 1 1
3 2 6 6
1 16 6
1 1 13 6 624
24 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
251 1 1 1
3 2 6 6
1 16 6
1 1 13 6 625
25 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
261 1 1 1
3 2 6 6
1 16 6
1 1 13 6 626
26 1 1 13 6 6
1 16 6
1 1 12 6 6
0 1 0 0.32
1 0 0 0 0 0.33
0 0 0 0 0.121
0 0 0 1 0.14
0 0 0 0 0 0.01
0 0 0 0 0.08
S en
Aleksandar MilinkovićElektrotehnički fakultet
10/16
PageRank Algoritam – model 4
01 1
3 6
16
160
0 1 13 6
1 13 6
16
0 0 1 0 0 0.17
1 0 0 0 0 0 0.17
0 1 0 0 0 0 0.171
0 0 0 0 0 0.17
0 0 0 0 1 0.17
0 0 0 0 1 0 0.17
S en
11 1
3 6
16
161
1 1 13 6
1 13 6
16
0 0 1 0 0 0.22
1 0 0 0 0 0 0.17
0 1 0 0 0 0 0.171
0 0 0 0 0 0.06
0 0 0 0 1 0.22
0 0 0 0 1 0 0.17
S en
21 1
3 6
16
162
2 1 13 6
1 13 6
16
0 0 1 0 0 0.11
1 0 0 0 0 0 0.22
0 1 0 0 0 0 0.171
0 0 0 0 0 0.06
0 0 0 0 1 0.22
0 0 0 0 1 0 0.22
S en
31 1
3 6
16
163
3 1 13 6
1 13 6
16
0 0 1 0 0 0.11
1 0 0 0 0 0 0.11
0 1 0 0 0 0 0.221
0 0 0 0 0 0.06
0 0 0 0 1 0.28
0 0 0 0 1 0 0.22
S en
41 1
3 6
16
164
4 1 13 6
1 13 6
16
0 0 1 0 0 0.13
1 0 0 0 0 0 0.11
0 1 0 0 0 0 0.111
0 0 0 0 0 0.07
0 0 0 0 1 0.30
0 0 0 0 1 0 0.28
S en
51 1
3 6
16
165
5 1 13 6
1 13 6
16
0 0 1 0 0 0.11
1 0 0 0 0 0 0.13
0 1 0 0 0 0 0.111
0 0 0 0 0 0.04
0 0 0 0 1 0.31
0 0 0 0 1 0 0.30
S en
61 1
3 6
16
166
6 1 13 6
1 13 6
16
0 0 1 0 0 0.07
1 0 0 0 0 0 0.11
0 1 0 0 0 0 0.131
0 0 0 0 0 0.04
0 0 0 0 1 0.33
0 0 0 0 1 0 0.31
S en
71 1
3 6
16
167
7 1 13 6
1 13 6
16
0 0 1 0 0 0.08
1 0 0 0 0 0 0.07
0 1 0 0 0 0 0.111
0 0 0 0 0 0.04
0 0 0 0 1 0.36
0 0 0 0 1 0 0.33
S en
81 1
3 6
16
168
8 1 13 6
1 13 6
16
0 0 1 0 0 0.08
1 0 0 0 0 0 0.08
0 1 0 0 0 0 0.071
0 0 0 0 0 0.04
0 0 0 0 1 0.37
0 0 0 0 1 0 0.36
S en
91 1
3 6
16
169
9 1 13 6
1 13 6
16
0 0 1 0 0 0.06
1 0 0 0 0 0 0.08
0 1 0 0 0 0 0.081
0 0 0 0 0 0.02
0 0 0 0 1 0.38
0 0 0 0 1 0 0.37
S en
101 1
3 6
16
1610
10 1 13 6
1 13 6
16
0 0 1 0 0 0.05
1 0 0 0 0 0 0.06
0 1 0 0 0 0 0.081
0 0 0 0 0 0.03
0 0 0 0 1 0.40
0 0 0 0 1 0 0.38
S en
111 1
3 6
16
1611
11 1 13 6
1 13 6
16
0 0 1 0 0 0.05
1 0 0 0 0 0 0.05
0 1 0 0 0 0 0.061
0 0 0 0 0 0.03
0 0 0 0 1 0.41
0 0 0 0 1 0 0.40
S en
121 1
3 6
16
1612
12 1 13 6
1 13 6
16
0 0 1 0 0 0.05
1 0 0 0 0 0 0.05
0 1 0 0 0 0 0.051
0 0 0 0 0 0.02
0 0 0 0 1 0.42
0 0 0 0 1 0 0.41
S en
131 1
3 6
16
1613
13 1 13 6
1 13 6
16
0 0 1 0 0 0.04
1 0 0 0 0 0 0.05
0 1 0 0 0 0 0.051
0 0 0 0 0 0.02
0 0 0 0 1 0.43
0 0 0 0 1 0 0.42
S en
141 1
3 6
16
1614
14 1 13 6
1 13 6
16
0 0 1 0 0 0.03
1 0 0 0 0 0 0.04
0 1 0 0 0 0 0.051
0 0 0 0 0 0.02
0 0 0 0 1 0.44
0 0 0 0 1 0 0.43
S en
151 1
3 6
16
1615
15 1 13 6
1 13 6
16
0 0 1 0 0 0.03
1 0 0 0 0 0 0.03
0 1 0 0 0 0 0.041
0 0 0 0 0 0.02
0 0 0 0 1 0.44
0 0 0 0 1 0 0.44
S en
161 1
3 6
16
1616
16 1 13 6
1 13 6
16
0 0 1 0 0 0.03
1 0 0 0 0 0 0.03
0 1 0 0 0 0 0.031
0 0 0 0 0 0.01
0 0 0 0 1 0.45
0 0 0 0 1 0 0.44
S en
171 1
3 6
16
1617
17 1 13 6
1 13 6
16
0 0 1 0 0 0.02
1 0 0 0 0 0 0.03
0 1 0 0 0 0 0.031
0 0 0 0 0 0.01
0 0 0 0 1 0.45
0 0 0 0 1 0 0.45
S en
181 1
3 6
16
1618
18 1 13 6
1 13 6
16
0 0 1 0 0 0.02
1 0 0 0 0 0 0.02
0 1 0 0 0 0 0.031
0 0 0 0 0 0.01
0 0 0 0 1 0.46
0 0 0 0 1 0 0.45
S en
191 1
3 6
16
1619
19 1 13 6
1 13 6
16
0 0 1 0 0 0.02
1 0 0 0 0 0 0.02
0 1 0 0 0 0 0.021
0 0 0 0 0 0.01
0 0 0 0 1 0.46
0 0 0 0 1 0 0.46
S en
201 1
3 6
16
1620
20 1 13 6
1 13 6
16
0 0 1 0 0 0.02
1 0 0 0 0 0 0.02
0 1 0 0 0 0 0.021
0 0 0 0 0 0.01
0 0 0 0 1 0.47
0 0 0 0 1 0 0.46
S en
211 1
3 6
16
1621
21 1 13 6
1 13 6
16
0 0 1 0 0 0.02
1 0 0 0 0 0 0.02
0 1 0 0 0 0 0.021
0 0 0 0 0 0.01
0 0 0 0 1 0.47
0 0 0 0 1 0 0.47
S en
221 1
3 6
16
1622
22 1 13 6
1 13 6
16
0 0 1 0 0 0.01
1 0 0 0 0 0 0.02
0 1 0 0 0 0 0.021
0 0 0 0 0 0.01
0 0 0 0 1 0.47
0 0 0 0 1 0 0.47
S en
231 1
3 6
16
1623
23 1 13 6
1 13 6
16
0 0 1 0 0 0.01
1 0 0 0 0 0 0.01
0 1 0 0 0 0 0.021
0 0 0 0 0 0.01
0 0 0 0 1 0.48
0 0 0 0 1 0 0.47
S en
241 1
3 6
16
1624
24 1 13 6
1 13 6
16
0 0 1 0 0 0.01
1 0 0 0 0 0 0.01
0 1 0 0 0 0 0.011
0 0 0 0 0 0.01
0 0 0 0 1 0.48
0 0 0 0 1 0 0.48
S en
251 1
3 6
16
1625
25 1 13 6
1 13 6
16
0 0 1 0 0 0.01
1 0 0 0 0 0 0.01
0 1 0 0 0 0 0.011
0 0 0 0 0 0.00
0 0 0 0 1 0.48
0 0 0 0 1 0 0.48
S en
261 1
3 6
16
1626
26 1 13 6
1 13 6
16
0 0 1 0 0 0.01
1 0 0 0 0 0 0.01
0 1 0 0 0 0 0.011
0 0 0 0 0 0.00
0 0 0 0 1 0.48
0 0 0 0 1 0 0.48
S en
271 1
3 6
16
1627
27 1 13 6
1 13 6
16
0 0 1 0 0 0.01
1 0 0 0 0 0 0.01
0 1 0 0 0 0 0.011
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.48
S en
281 1
3 6
16
1628
28 1 13 6
1 13 6
16
0 0 1 0 0 0.01
1 0 0 0 0 0 0.01
0 1 0 0 0 0 0.011
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.49
S en
291 1
3 6
16
1629
29 1 13 6
1 13 6
16
0 0 1 0 0 0.01
1 0 0 0 0 0 0.01
0 1 0 0 0 0 0.011
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.49
S en
301 1
3 6
16
1630
30 1 13 6
1 13 6
16
0 0 1 0 0 0.01
1 0 0 0 0 0 0.01
0 1 0 0 0 0 0.011
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.49
S en
311 1
3 6
16
1631
31 1 13 6
1 13 6
16
0 0 1 0 0 0.00
1 0 0 0 0 0 0.01
0 1 0 0 0 0 0.011
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.49
S en
321 1
3 6
16
1632
32 1 13 6
1 13 6
16
0 0 1 0 0 0.00
1 0 0 0 0 0 0.00
0 1 0 0 0 0 0.011
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.49
S en
331 1
3 6
16
1633
33 1 13 6
1 13 6
16
0 0 1 0 0 0.00
1 0 0 0 0 0 0.00
0 1 0 0 0 0 0.001
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.49
S en
341 1
3 6
16
1634
34 1 13 6
1 13 6
16
0 0 1 0 0 0.00
1 0 0 0 0 0 0.00
0 1 0 0 0 0 0.001
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.49
S en
351 1
3 6
16
1635
35 1 13 6
1 13 6
16
0 0 1 0 0 0.00
1 0 0 0 0 0 0.00
0 1 0 0 0 0 0.001
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.49
S en
361 1
3 6
16
1636
36 1 13 6
1 13 6
16
0 0 1 0 0 0.00
1 0 0 0 0 0 0.00
0 1 0 0 0 0 0.001
0 0 0 0 0 0.00
0 0 0 0 1 0.49
0 0 0 0 1 0 0.49
S en
371 1
3 6
16
1637
37 1 13 6
1 13 6
16
0 0 1 0 0 0.00
1 0 0 0 0 0 0.00
0 1 0 0 0 0 0.001
0 0 0 0 0 0.00
0 0 0 0 1 0.50
0 0 0 0 1 0 0.49
S en
381 1
3 6
16
1638
38 1 13 6
1 13 6
16
0 0 1 0 0 0.00
1 0 0 0 0 0 0.00
0 1 0 0 0 0 0.001
0 0 0 0 0 0.00
0 0 0 0 1 0.50
0 0 0 0 1 0 0.50
S en
391 1
3 6
16
1639
39 1 13 6
1 13 6
16
0 0 1 0 0 0.00
1 0 0 0 0 0 0.00
0 1 0 0 0 0 0.001
0 0 0 0 0 0.00
0 0 0 0 1 0.50
0 0 0 0 1 0 0.50
S en
Aleksandar MilinkovićElektrotehnički fakultet
11/16
Nema visećih čvorova, ali E i F formiraju ciklus
Zajedno apsorbuju sve rangove
Uvodi se α – dumping factor – [0,1]
Predstavlja procenat out link vrednosti
Ostatak se ravnopravno raspoređuje na sve stranice
α ≈ 85% dalje najbolji rezultat
PageRank Algoritam – model 5
1(1 )( ee )TG S
n
Aleksandar MilinkovićElektrotehnički fakultet
12/16
PageRank Algoritam – model 5
00
0.17
0.17
0.171
0.17
0.17
0.17
G en
11
0.21
0.17
0.171
0.07
0.21
0.17
G en
22
0.13
0.21
0.171
0.07
0.21
0.21
G en
33
0.13
0.14
0.201
0.07
0.25
0.21
G en
44
0.14
0.14
0.141
0.08
0.26
0.24
G en
55
0.14
0.15
0.141
0.07
0.27
0.24
G en
66
0.12
0.14
0.151
0.07
0.27
0.25
G en
77
0.12
0.13
0.141
0.07
0.28
0.26
G en
88
0.12
0.13
0.131
0.07
0.28
0.26
G en
99
0.12
0.13
0.141
0.06
0.29
0.27
G en
1010
0.12
0.13
0.141
0.06
0.29
0.27
G en
1111
0.12
0.12
0.131
0.06
0.29
0.27
G en
1212
0.12
0.12
0.131
0.06
0.29
0.27
G en
1313
0.12
0.12
0.131
0.06
0.29
0.27
G en
1414
0.11
0.12
0.131
0.06
0.30
0.28
G en
1515
0.11
0.12
0.131
0.06
0.30
0.28
G en
1616
0.11
0.12
0.131
0.06
0.30
0.28
G en
1717
0.11
0.12
0.131
0.06
0.30
0.28
G en
1818
0.11
0.12
0.131
0.06
0.30
0.28
G en
1919
0.11
0.12
0.131
0.06
0.30
0.28
G en
Brza konvergencija!
Aleksandar MilinkovićElektrotehnički fakultet
13/16
Matrica je gusta matrica
Složenost množenja je
Računanje
G
G 2( )O n1
(1 )( ee )TG Sn
1k kG
1 TS H ean
Matrica G nije potrebna!
H je vrlo retka matrica
Vremenska složenost množenja je ( )O n
Aleksandar MilinkovićElektrotehnički fakultet
14/16
PageRank dobar za indeksiranje strukture
Predstavlja reputaciju stranice
Ukupno rangiranje zavisi i od sadržaja
Indeksiranje se radi off-line
Na PageRank je teško uticati
Na ukupno rangiranje može preko SEO
Zaključak
Aleksandar MilinkovićElektrotehnički fakultet
15/16
PigeonRank
Aleksandar MilinkovićElektrotehnički fakultet
16/16
1. S. Brin and L. Page, “The anatomy of a large-scale hypertextual Web search engine,” Computer Networks and ISDN Systems, vol. 33, pp. 107–117, 1998.
2. A. N. Langville and C. D. Meyer, “Deeper inside PageRank,” Internet Mathematics, vol. 1, no. 3, pp. 335–380, 2004.
3. P. Berkhin, “A survey on PageRank computing,” Internet Mathematics, vol. 2, no. 1, pp. 73–120, 2005.
4. S. Serra-Capizzano, “Jordan canonical form of the Google matrix: a potential contribution to the PageRank computation,” SIAM J. Matrix Anal. Appl., vol. 27, no. 2, pp. 305–312, 2005.
5. A. N. Langville and C. D. Meyer, Google’s PageRank and beyond: The Science of Search Engine Rankings, Princeton University Press, 2006.
Literatura
Aleksandar MilinkovićElektrotehnički fakultet
Google-ov PageRank Algoritam
Aleksandar MilinkovićElektrotehnički fakultet u Beogradu