PageRank指導⽼老師 許慶昇 研究⽣生 鍾聖彥

Reference• Bing Liu (2011). Web Data Mining: Exploring Hyperlinks,

Contents, and Usage Data. 2nd Ed., Springer-Verlang Berlin Heigelberg.

• Page, Lawrence, et al. "The PageRank citation ranking: bringing order to the web." (1999).

• Brin, Sergey, and Lawrence Page. "The anatomy of a large-scale hypertextual Web search engine." Computer networks and ISDN systems 30.1 (1998): 107-117.

• PageRank，http://en.wikipedia.org/wiki/PageRank • 台灣搜尋引擎優化與⾏行銷研究院 - SEO & SEM Blog http://seo.dns.com.tw/ • Croft, W. Bruce, Donald Metzler, and Trevor Strohman. Search

engines: Information retrieval in practice. Reading: Addison-Wesley, 2010.

Why  This  Order?

PageRank was developed by Larry Page (hence the name Page-Rank) and Sergey Brin.

Not Page 1, 2, 3………

Larry Page• Born March 26, 1973(age 40)

• American computer scientist

• Co-founder and CEO of Google Inc.

• As of 2013, Page's personal wealth is estimated to be US$20.3 billion, ranking him #13 on the Forbes 400 list of the 400 richest Americans.

• Inventor of PageRank, the foundation of Google's search ranking algorithm.

Sergey Brin

• Born August 21, 1973

• Russian

• Co-founder of Google

• As of 2013, his personal wealth was estimated to be $24.4 billion.

What is PageRank ?

PageRank is able to order search results so that more important and central Web pages are given preference.(Sergey Brin, Lawrence Page，1998)

A method for rating the importance of web pages objectively and mechanically using the link structure of the web. (Sergey Brin, Lawrence Page，1998).

The year 1998 was an important year for web link analysis and web search(Bing Liu ，2011).

Applications

PageRank has applications in search, browsing, and traffic estimation.(Sergey Brin, Lawrence Page，1998).

To test the utility of PageRank for search, we built a web search engine called Google.(Sergey Brin, Lawrence Page，1998).

Link Structure of the Web

Backlinks and Forward links: !

A and B are C’s backlinks C is A and B’s forward link

Definition of PageRank

PageRank 的運算公式被設計為「⼀一個網站的 PageRank 值,來⾃自於加總所有連結到該網站的網站之 PageRank 值除以本⾝身的導出連結數」

Definition of PageRank

此公式是⼀一個會收斂的運算 以上述例⼦子,假設每個網⾴頁的 PageRank 值都是均等的,則計算⽅方法如下(每階段的 PR

值使⽤用前⼀一階段的運算 結果):

1. PR(A)=PR(B)=PR(C)=1/3=0.33 2. PR(A)=0.33 PR(B)=0.33/2=0.17 PR(C)=0.33/2+0.33=0.5 3. PR(A)=0.5 PR(B)= 0.33/2=0.17 PR(C)=0.33/2+0.17=0.33 4. PR(A)=0.33 PR(B)=0.5/2=0.25 PR(C)=0.5/2+0.17=0.42 5. 依此類推... 最後趨近: PR(A)=0.4 PR(B)=0.2 PR(C)=0.4 !

Convergence Properties

Definition of PageRank

A Simple Version of PageRank

u: a web page Bu: the set of u’s backlinks Nv: the number of forward links of page v c: the normalization factor to make ||R||L1 = 1 (||R||L1= |R1 + … + Rn|) (so that the total rank of all web pages is constant).

A Problem with Simplified PageRank

During each iteration, the loop accumulates rank but never distributes rank to other pages.

Random Surfer Model

The standing probability distribution of a random walk on the graph of the web. Simply keeps clicking successive links at random.

Modified Version of PageRank

E(u):The additional factor E can be viewed as a way of modeling this behavior: the surfer periodically “gets bored" and jumps to a random page chosen based on the distribution in E.

Searching with PageRank

Searching with PageRank

Reference• Bing Liu (2011). Web Data Mining: Exploring Hyperlinks,

Contents, and Usage Data. 2nd Ed., Springer-Verlang Berlin Heigelberg.

• Page, Lawrence, et al. "The PageRank citation ranking: bringing order to the web." (1999).

• Brin, Sergey, and Lawrence Page. "The anatomy of a large-scale hypertextual Web search engine." Computer networks and ISDN systems 30.1 (1998): 107-117.

• PageRank，http://en.wikipedia.org/wiki/PageRank • 台灣搜尋引擎優化與⾏行銷研究院 - SEO & SEM Blog http://seo.dns.com.tw/ • Croft, W. Bruce, Donald Metzler, and Trevor Strohman. Search

engines: Information retrieval in practice. Reading: Addison-Wesley, 2010.