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# PageRank, HITS and a unified framework for link analysis

siam international conference on data mining, pp.249-253, (2003)

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摘要

Two popular webpage ranking algorithms are HITS and PageRank. HITS emphasizes mutual reinforcement be- tween authority and hub webpages, while PageRank em- phasizes hyperlink weight normalization and web surf- ing based on random walk models. We systemati- cally generalize/combine these concepts into a unied framework. The ranking framewo...更多

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简介

- PageRank[1] and HITS (Hypertext Induced Topic Selection)[3]. HITS makes the crucial distinction of hubs and authorities and computes them in a mutually reinforcing way.
- In the HITS algorithm[3], each webpage i has both a hub score yi and an authority score xi .
- Since LTL determines the authority ranking, the authors call LTL the authority matrix.
- This shows the close relationship between authority and co-citation.
- Since LLT determines the hub scores, the authors call LLT the hub matrix.
- The authors prove that L LT = Dout + R, where Dout is the diagonal matrix containing out-degrees of all nodes, and R

重点内容

- PageRank[1] and HITS (Hypertext Induced Topic Selection)[3]
- We prove that LTL = Din + C, where Din is the diagonal matrix containing in-degrees of all nodes, and
- We prove that L LT = Dout + R, where Dout is the diagonal matrix containing out-degrees of all nodes, and R
- Assuming the web graph is a fixed degree sequence random graph, HITS results in average case can be solved in closed form [2], which proves that authority ranking by HITS
- Democracy: each website has a total of one vote. Another key feature is that PageRank adopts a web surfing model based on a Markov process in determining the scores:
- We propose to define hub in PageRank using the same random surfer model as in definition of authority

结果

- Is the co-reference matrix.
- This shows the close relationship between hubs and co-references.
- Assuming the web graph is a fixed degree sequence random graph, HITS results in average case can be solved in closed form [2], which proves that authority ranking by HITS
- Hub ranking in HITS is identical to the ranking by out-degrees.
- Vectors x = (x1 , · · · , xn ) and y = (y1 , · · · , yn ) contain the authority score and hub score of each webpage, respectively.
- Dout LDin conclude that even though PageRank and HITS
- HITS ranking and PageRank ranking are very similar, too.
- It has 4,906,214 websites and represents a site-level graph of the Web. Rankings are shown below.
- 2. Authority Ranking
- The key feature of PageRank is the hyperlink weight normalization, as shown in Fig.1 from the perspective of cocitation and co-reference.
- Another key feature is that PageRank adopts a web surfing model based on a Markov process in determining the scores:
- The equilibrium distribution of random surfers on webpages is a measure of a webpage’s “importance”, is the authority score in PageRank.
- The fact that the authors all make reference to a highly referenced site such as New York Times says little about whether the authors are similar.
- The authors propose to define hub in PageRank using the same random surfer model as in definition of authority.
- Hits InDgr Page www.runnersworld.com/
- Www.coolrunning.com/
- Www.kicksports.com/
- Www.halhigdon.com/
- Www.ontherun.com/
- Www.runningroom.com/

结论

- Www.adidas.com/
- The most important feature of HITS is the mutual reinforcement between hubs and authorities, while the most important feature of PageRank is the hyperlink weight normalization.
- The authors clarify and formalize weight propagation and random surfing as two different but related method to compute ranking scores.
- One can design new ranking algorithms.
- The authors study three new ranking algorithms: the AuthRank, the Hub-Rank and the Sym-Rank.
- HITS ranking and PageRank ranking are highly correlated with indegree ranking.

- Table1: Iop and Oop operations for HITS, PageRank, Auth-Rank, Hub-Rank, and Sym-Rank

引用论文

- S. Brin and L. Page. The anatomy of a large-scale hypertextual web search engine. Proc. of 7th WWW Conferece, 1998.
- C. Ding, H. Zha, X. He, P. Husbands, and H. Simon. Analysis of hubs and authorities on the web. Lawrence Berkeley Nat’l Lab Tech Report 47847, May 2001.
- J. M. Kleinberg. Authoritative sources in a hyperlinked environment. J. ACM, 48:604–632, 1999.

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