1. HITS Hypertext-Induced Topic Selection
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SELİME IŞIK
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OUTLINE
Introduction
PageRank Algorithm
HITS Algorithm
HITS Example
HITS vs PageRank
Conclusion
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Search Engines
1.Crawler: retrieves the contents of web pages
2.Indexer: stores and indexes information on the retrieved pages
3.Ranker: determines the importance of web pages returned
4.Retrieval Engine: performs lookups on index tables
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Ranking
Today’s search engines may return millions
of pages for a certain query
It is not possible for a user to preview all the returned results
So, ranking is helpful
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Rankers
Rankers are classified into two groups :
1.Content-based rankers
number of matched terms
frequency of terms
location of terms
2.Connectivity-based rankers
links that point to them
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Link Analysis
There are two famous link analysis methods:
1.PageRank Algorithm
2.HITS Algorithm
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PageRank
originally formulated by Sergey Brin and Larry Page
does not rank web sites as a whole but is determined for each page individually according to their authoritativeness
if an authoritative web page A links to page B, then B is also authoritative
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PageRank (2)
recursive formula
page rank initially 1 for all nodes
normalized when difference between two successive calculations is very small
PR(A) = (1-d) + d (PR(T1)/C(T1) PR(Tn)/C(Tn))
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HITS
Kleinberg's hypertext-induced topic selection (HITS) algorithm is also developed for ranking documents based on the link information among a set of documents.
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Authorities and hubs
The algorithm produces two types of pages:
- Authority: pages that provide an important, trustworthy information on a given topic
- Hub: pages that contain links to authorities
Authorities and hubs exhibit a mutually reinforcing relationship: a better hub points to many good authorities, and a better authority is pointed to by many good hubs
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11. Authorities and hubs (2)
a(1) = h(2) + h(3) + h(4) h(1) = a(5) + a(6) + a(7) 1 5 6 7 2 3 4
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Definitions
Authority: pages that provide an important, trustworthy information on a given topic
Hubs: pages that contain links to authorities
Indegree: number of incoming links to a given node, used to measure the authoritativeness
Outdegree: number of outgoing links from a given node, here it is used to measure the hubness
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HITS Algorithm
Hubs point to lots of authorities.
Authorities are pointed to by lots of hubs.
Together they form a bipartite graph:
Hubs Authorities
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Step By Step HITS-1
determines a base set S
let set of documents returned by a standard search engine be called the root set R
Initialize S to R
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Step By Step HITS - 2
Add to S all pages pointed to by any page in R.
Add to S all pages that point to any page in R
Maintain for each page p in S:
Authority score: ap (vector a)
Hub score: hp (vector h)
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Step By Step HITS - 3
For each node initiliaze the ap and hp to 1/n
In each iteration calculate the authority weight for each node in S
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Step By Step HITS - 4
In each iteration calculate the hub weight for each node in S
Note: The hub weights are computed from the current authority weights, which were computed from the previous hub weights.
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Step By Step HITS - 5
After new weights are computed for all nodes, the weights are normalized:
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19. Convergence of HITS Algorithm
Let A be an adjacency matrix of S
Aij = 1 for i S , jS if and only if i->j
Authority and hub:
ak = φkAThk-1; hk = ψkAak;
Combination of both formulas gives:
ak = φkψk-1ATAak for k > 1
hk = ψkφkAAThk for k > 0
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20. Convergence of HITS Algorithm-2
The algorithm converges to a fixed point if iterated indefinitely and the resulting authority and hub vectors satisfy
a* = (1/µ*)ATAa*; h* = (1/µ*)AATh*;
The authority vector a* is an eigenvector of ATA ,converging to ATA
The hub vector h* is an eigenvector of AAT, converging to AAT
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The Pseudocode of HITS
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HITS Example
Root Set R {1,2,3,4}
Extend it to form the base set S
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HITS Example Results
Authority
Authority and Hubness Weight
Hubness
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HITS vs PageRank
HITS emphasizes mutual reinforcement between authority and hub webpages, while PageRank does not attempt to capture the distinction between hubs and authorities. It ranks pages just by authority.
HITS is applied to the local neighborhood of pages surrounding the results of a query whereas PageRank is applied to the entire web
HITS is query dependent but PageRank is query-independent
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HITS vs PageRank (2)
Both HITS and PageRank correspond to matrix computations.
Both can be unstable: changing a few links can lead to quite different rankings.
PageRank doesn't handle pages with no outedges very well, because they decrease the PageRank overall
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Conclusion
HITS is a general algorithm used for calculating the authority and hubs in order to rank the retrieved data
The basic aim of that algorithm is to induce the Web graph by finding set of pages with a search on a given topic (query).
Results demonstrates that it is good in calculating the authority nodes and hubness.
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References
Engines
research.microsoft.com/users/tyliu/files/USTC-Lecture-tyliu.ppt
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THANK YOU 
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ANY QUESTIONS?
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