Hubs and Authorities on the

photofitterInternet and Web Development

Dec 4, 2013 (3 years and 9 months ago)

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Hubs and Authorities on the
world wide web

(most from Rao’s lecture slides)

Presentor: Lei Tang

Desiderata for link
-
based ranking


A page that is referenced by lot of important pages (has more
back links
) is more important (Authority)


A page referenced by a single important page may be more
important than that referenced by five unimportant pages


No links between competitive authorities(like Ford, Honda)


A page that references a lot of important pages is also important
(Hub)


Good authoritative pages (
authorities
) and good hub pages
(
hubs
) reinforce each other.


“Importance” can be propagated



Your importance is the weighted sum of the importance
conferred on you by the pages that refer to you


The importance you confer on a page may be proportional
to how many other pages you refer to (cite)


(Also what you say about them when you cite them!)


Different

Notions of

importance

Authority and Hub Pages (2)


Authorities and hubs related to the same query
tend to form a bipartite subgraph of the web
graph.








A web page can be a good authority and a
good hub.

hubs

authorities

Authority and Hub Pages (7)

Operation I: for each page p:




a(p) =

†††
栨焩

††††††††
焺q⡱Ⱐ瀩

E


Operation O: for each page p:




h(p) =

††††
愨焩

††††††††
焺q⡰Ⱐ焩

E


q
1

q
2

q
3

p

q
3

q
2

q
1

p

Authority and Hub Pages (8)

Matrix representation of operations I and O.

Let A be the adjacency

matrix of SG: entry (p, q) is
1 if p has a link to q, else the entry is 0.

Let A
T

be the transpose of A.

Let h
i

be vector of hub scores after i iterations.

Let a
i

be the vector of authority scores after i
iterations.


Operation I: a
i

= A
T

h
i
-
1


Operation O: h
i

= A a
i

1
1




i
T
i
i
T
i
h
AA
h
Aa
A
a




0
0
h
AA
h
a
A
A
a
i
T
i
i
T
i


Normalize after every multiplication

Authority and Hub Pages (11)

Example: Initialize all scores to 1.

1
st

Iteration:


I operation:


a(q
1
) = 1, a(q
2
) = a(q
3
) = 0,


a(p
1
) = 3, a(p
2
) = 2


O operation: h(q
1
) = 5,


h(q
2
) = 3, h(q
3
) = 5, h(p
1
) = 1, h(p
2
) = 0


Normalization: a(q
1
) = 0.267, a(q
2
) = a(q
3
) = 0,


a(p
1
) = 0.802, a(p
2
) = 0.535, h(q
1
) = 0.645,


h(q
2
) = 0.387, h(q
3
) = 0.645, h(p
1
) = 0.129, h(p
2
)
= 0

q
1

q
2

q
3

p
1

p
2

Authority and Hub Pages (12)

After 2 Iterations:


a(q
1
) = 0.061, a(q
2
) = a(q
3
) = 0, a(p
1
) = 0.791,


a(p
2
) = 0.609, h(q
1
) = 0.656, h(q
2
) = 0.371,


h(q
3
) = 0.656, h(p
1
) = 0.029, h(p
2
) = 0

After 5 Iterations:


a(q
1
) = a(q
2
) = a(q
3
) = 0,


a(p
1
) = 0.788, a(p
2
) = 0.615


h(q
1
) = 0.657, h(q
2
) = 0.369,


h(q
3
) = 0.657, h(p
1
) = h(p
2
) = 0

q
1

q
2

q
3

p
1

p
2

(why) Does the procedure converge?

0
0
2
1
2
0
1
)
(
x
M
x
x
M
Mx
x
AA
M
Mx
x
k
k
T





x

x
2

x
k



1
0
2
2
1
1
0
1
1
1
1
1
2
1
1
2
1
)
...
),
,...
,
(
]
ˆ
...
ˆ
ˆ
[
ˆ
ˆ
...
ˆ
ˆ
2
1
2
1
2
1
e
x
M
e
c
e
c
e
c
x
E
E
E
E
M
E
E
E
E
E
E
M
E
E
M
k
n
n
k
k
k
k
k
diag
e
e
e
n
n
n








































The rate of convergence depends on the “eigen gap”

2
1



Authority and Hub Pages (3)

Main steps of the algorithm for finding good authorities
and hubs related to a query
q
.

1.
Submit
q

to a regular similarity
-
based search
engine. Let
S

be the set of top n pages returned
by the search engine. (
S

is called the
root set

and
n is often in the low hundreds).

2.
Expand
S

into a large set T (
base set
):


Add pages that are pointed to by any page in
S
.


Add pages that point to any page in
S
.


If a page has too many parent pages, only the first k
parent pages will be used for some k.

Authority and Hub Pages (4)

3. Find the subgraph SG of the web graph that is
induced by T.

S

T

Authority and Hub Pages (5)

Steps 2 and 3 can be made easy by
storing the link structure of the
Web in advance Link structure
table (during crawling)


--
Most search engines serve this
information now. (e.g. Google’s
link: search)



parent_url child_url


url1 url2


url1 url3



Authority and Hub Pages (6)

4.
Compute the authority score and hub score of
each web page in T based on the subgraph
SG(V,
E).


Given a page p, let


a(p)

be the authority score of p


h(p)

be the hub score of p


(
p, q
) be a directed edge in E from p to q.


Two basic operations:


Operation I: Update each a(p) as the sum of all
the hub scores of web pages that point to p.


Operation O: Update each h(p) as the sum of all
the authority scores of web pages pointed to by p.

Authority and Hub Pages (9)


After each iteration of applying Operations I
and O, normalize all authority and hub scores.






Repeat until the scores for each page
converge (the convergence is guaranteed).

5. Sort pages in descending authority scores.

6. Display the top authority pages.






V
q
q
a
p
a
p
a
2
)
(
)
(
)
(





V
q
q
h
p
h
p
h
2
)
(
)
(
)
(
Authority and Hub Pages (10)

Algorithm (summary)


submit q to a search engine to obtain the root
set S;


expand S into the base set T;


obtain the induced subgraph SG(V, E) using T;


initialize a(p) = h(p) = 1 for all p in V;


for each p in V until the scores converge


{ apply Operation I;


apply Operation O;


normalize a(p) and h(p);

}


return pages with top authority scores;

Handling “spam” links

Should all links be equally treated?

Two considerations:


Some links may be more
meaningful/important than other links.


Web site creators may trick the system to
make their pages more authoritative by
adding dummy pages pointing to their
cover pages (spamming).


Handling Spam Links (contd)


Transverse link:

links between pages with
different domain names.

Domain name:

the first level of the URL of a page.


Intrinsic link:

links between pages with the
same domain name.

Transverse links are more important than
intrinsic links.

Two ways to incorporate this:

1.
Use only transverse links and discard
intrinsic links.

2.
Give lower weights to intrinsic links.

Handling Spam Links (contd)

How to give lower weights to intrinsic
links?

In adjacency matrix A, entry (p, q) should
be assigned as follows:


If p has a transverse link to q, the entry
is 1.


If p has an intrinsic link to q, the entry is
c, where 0 < c < 1.


If p has no link to q, the entry is 0.

Considering link “context”

For a given link (p, q), let
V(p, q)

be the vicinity
(e.g.,


㔰5捨慲c捴c牳潦瑨攠汩湫n


If
V(p, q)

contains terms in the user query
(topic), then the link should be more useful
for identifying authoritative pages.


To incorporate this: In adjacency matrix
A
,
make the weight associated with link
(p, q)

to
be
1+n(p, q),



where n(p, q) is the number of terms in V(p, q) that appear
in the query.


Alternately, consider the “vector similarity” between
V(p,q) and the query Q

Evaluation

Sample experiments:


Rank based on large in
-
degree (or backlinks)


query: game

Rank in
-
degree URL


1 13
http://www.gotm.org


2 12
http://www.gamezero.com/team
-
0/


3 12
http://ngp.ngpc.state.ne.us/gp.html


4 12
http://www.ben2.ucla.edu/~permadi/


gamelink/gamelink.html


5 11
http://igolfto.net/


6 11
http://www.eduplace.com/geo/indexhi.html


Only pages 1, 2 and 4 are authoritative game pages.

Evaluation

Sample experiments (continued)


Rank based on large authority score.


query: game

Rank Authority URL


1 0.613
http://www.gotm.org


2 0.390
http://ad/doubleclick/net/jump/


gamefan
-
network.com/


3 0.342
http://www.d2realm.com/


4 0.324
http://www.counter
-
strike.net


5 0.324
http://tech
-
base.com/


6 0.306
http://www.e3zone.com


All pages are authoritative game pages.

Authority and Hub Pages (19)

Sample experiments (continued)


Rank based on large authority score.


query: free email

Rank Authority URL


1 0.525
http://mail.chek.com/


2 0.345
http://www.hotmail/com/


3 0.309
http://www.naplesnews.net
/


4 0.261
http://www.11mail.com/


5 0.254
http://www.dwp.net/


6 0.246
http://www.wptamail.com/


All pages are authoritative free email pages.

Tyranny of Majority

1

2

3

4

6

7

8

5

Which do
you

think are

Authoritative pages?

Which are good hubs?


-
intutively, we would say


that 4,8,5 will be authoritative


pages and 1,2,3,6,7 will be


hub pages.


BUT

The power iteration will show that

Only 4 and 5 have non
-
zero authorities

[.923 .382]

And only 1, 2 and 3 have non
-
zero hubs

[.5 .7 .5]

Tyranny of Majority (explained)

p1

p2

pm

p

q1

qn

q

m

n

Suppose h0 and a0 are all initialized to 1

2
2
1
2
2
1
1
1
)
(
)
(
)
(
)
(
n
m
n
q
a
n
m
m
p
a
normalized
n
q
a
m
p
a






2
2
1
2
2
1
)
(
)
(
n
m
n
q
h
n
m
m
p
h
i
i




2
2
2
2
2
2
2
2
2
2
2
)
(
)
(
)
(
)
(











m
n
p
a
q
a
n
m
n
q
a
n
m
m
p
a
0
)
(
)
(








k
k
k
m
n
p
a
q
a
m>n

Impact of Bridges..

1

2

3

4

6

7

8

5

When the graph is disconnected,

only 4 and 5 have non
-
zero authorities

[.923 .382]

And only 1, 2 and 3 have non
-
zero hubs

[.5 .7 .5]CV

9

When the components are bridged by adding one page (9)

the authorities change

only 4, 5 and 8 have non
-
zero authorities

[.853 .224 .47]

And 1, 2, 3, 6,7 and 9 will have non
-
zero hubs

[.39 .49 .39 .21 .21 .6]

Authority and Hub Pages (24)

Multiple Communities (continued)


How to retrieve pages from smaller communities?


A method for finding pages in nth largest community:


Identify the next largest community using the existing
algorithm.


Destroy this community by removing links associated
with pages having large authorities.


Reset all authority and hub values back to 1 and
calculate all authority and hub values again.


Repeat the above n


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捯浭畮楴cw楬i扥b瑨攠湴栠污牧敳琠捯浭畮楴c.

Multiple Clusters on “House”

Query: House (first community)

Authority and Hub Pages (26)

Query: House (second community)

More stable because


random surfer model


allows low prob edges


to every place.CV

Can be done

For base set too


Can be done

For full web too


Can be made stable with subspace
-
based

A/H values [see Ng. et al.; 2001]

See topic
-
specific

Page
-
rank idea..

Novel uses of Link Analysis


Link analysis algorithms

HITS, and
Pagerank

are not limited to hyperlinks

-
Citeseer/Cora use them for analyzing citations
(the link is through “citation”)

-
See the irony here

link analysis ideas originated from
citation analysis, and are now being applied for citation
analysis



-
Some new work on “keyword search on
databases” uses foreign
-
key links and link
analysis to decide which of the tuples matching
the keyword query are most important (the link is
through foreign keys)

-
[
Sudarshan et. Al. ICDE 2002
]

-
Keyword search on databases is useful to make
structured databases accessible to naïve users who don’t
know structured languages (such as SQL).