Fermat's theorem on sums of two squares: Difference between revisions

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'''Hyperlink-Induced Topic Search''' ('''HITS'''; also known as '''hubs and authorities''') is a [[link analysis]] [[algorithm]] that rates Web pages, developed by [[Jon Kleinberg]].  It was a precursor to [[PageRank]]. The idea behind Hubs and Authorities stemmed from a particular insight into the creation of web pages when the Internet was originally forming; that is, certain web pages, known as hubs, served as large directories that were not actually authoritative in the information that it held, but were used as compilations of a broad catalog of information that led users directly to other authoritative pages. In other words, a good hub represented a page that pointed to many other pages, and a good authority represented a page that was linked by many different hubs.<ref>{{cite web
== afraid of crime than others sad ==
  | authors = Christopher D. Manning, Prabhakar Raghavan & Hinrich Schütze
  | title = Introduction to Information Retrieval
  | publisher = Cambridge University Press
  | year = 2008
  | url = http://nlp.stanford.edu/IR-book/html/htmledition/hubs-and-authorities-1.html
  | doi =  
  | accessdate = 2008-11-09}}</ref>


The scheme therefore assigns two scores for each page: its authority, which estimates the value of the content of the page, and its hub value, which estimates the value of its links to other pages.
The level is also able to push on the push, their hearts more clearly, the kind of people who commit crimes than their whatever, [http://www.dmwai.com/webalizer/kate-spade-6.html ケイトスペード マザーズバッグ] but like this mimicking 'whoring' was ripped off, and would not give sympathy and concern, at most, give evaluation : deserve.<br><br>'head back ...... there is a second case in return?' I asked the crime.<br><br>'Yes, I went to the police station, they gave me one who sinks the 80,000 special smile stomach ache ...... what drops, do not laugh at me silly chant, and later gave registered under, let me come back to other news , First Nima did not sound a. 'big golden bowl depressed authentic.<br><br>when he looked over [http://www.dmwai.com/webalizer/kate-spade-9.html ケイトスペード 財布 値段] the crime, a look of sorrow over sin, but he was afraid to ask the whereabouts [http://www.dmwai.com/webalizer/kate-spade-10.html kate spade ハンドバッグ] of stolen property. More than sin and my heart was thinking, maybe not suspect too clever, but too many police lengthy and bureaucratic oversight, let fraud become so at ease.<br><br>asked a few details, all the recordings, got up to leave, afraid of crime [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード バッグ ショルダー] than others sad, straight put down the sentence: 'I'm sorry, Wan master, we already have a lot of information to [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード バッグ アウトレット] find the vehicle will contact you, probably more trouble you several times, you do not mind ah
相关的主题文章：
<ul>
 
  <li>[http://lianshoutuan.com/plus/view.php?aid=10418 http://lianshoutuan.com/plus/view.php?aid=10418]</li>
 
  <li>[http://ywnfs.com/plus/feedback.php?aid=121 http://ywnfs.com/plus/feedback.php?aid=121]</li>
 
  <li>[http://bbs.unmegame.com/forum.php?mod=viewthread&tid=1042364 http://bbs.unmegame.com/forum.php?mod=viewthread&tid=1042364]</li>
 
</ul>


==History==
== 'I will not do anything ...... ==


===In journals===
, Also boast Xiong Jianfei lot, boast not know exactly how everyone was a different story.<br><br>Implying really struggling to find a police force, we are qualified?<br><br>wrong, there is one more than the crime, this time only to find 许平秋 is skipped over sin praise of others, finished just turned around and asked more than crime, [http://www.dmwai.com/webalizer/kate-spade-11.html ケイトスペード 財布 通販] very puzzled and asked the remainder of [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペードニューヨーク 財布] sin and said: 'I sin, what are you doing up how the family did not get you? too much information. '<br><br>that ask a lot of people have brought to my heart, and fear that ticket event was tugging, I honestly sin scratched his head, carrying innocent eyes, make life difficult for typical sentence: 'I will [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペードショルダーバッグ新作] not do anything ...... , they rely on, that ...... they mix down several financial aid. '<br><br>'Oh ......' Xu Pingqiu like to believe, but once again asked: '? Then how do you find them.'<br><br>'I [http://www.dmwai.com/webalizer/kate-spade-8.html kate spade 財布 ゴールド] see a beautiful sister who appeared in front of me twice ...... The sister and my dreams almost exactly the same, I suddenly love at first sight, I will chase wanted to see her in the end who is? [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペード クラッチバッグ] have not opportunities for taking a dip, the results did not
Formerly, many methods were used for ranking the importance of scientific journals. One such method was Garfield's [[impact factor]]. However, many journals such as Science and  Nature are filled with numerous citations, making these magazines have very high impact factors. Thus, when comparing two more obscure journals which have received roughly the same number of citations but one of these journals has received many citations from Science and Nature, this journal needs be ranked higher. In other words, it is better to receive citations from an important journal than from an unimportant one.<ref>{{cite web
相关的主题文章：
   | last = Kleinberg
<ul>
  | first = Jon
    
   | authorlink =
  <li>[http://www.bjl5555.com/forum.php?mod=viewthread&tid=109595 http://www.bjl5555.com/forum.php?mod=viewthread&tid=109595]</li>
  | coauthors =  
    
  | title = Hubs, Authorities, and Communities
  <li>[http://www.dzghome.com/forum.php?mod=viewthread&tid=153188 http://www.dzghome.com/forum.php?mod=viewthread&tid=153188]</li>
  | work =
    
  | publisher = Cornell University
  <li>[http://www.astrostreasurechest.net/cgi/guestbook.cgi http://www.astrostreasurechest.net/cgi/guestbook.cgi]</li>
   | date = December 1999
    
  | url = http://www.cs.brown.edu/memex/ACM_HypertextTestbed/papers/10.html
</ul>
   | doi =
  | accessdate = 2008-11-09}}</ref>


===On the Web===
== . 'willing to be money ==
This phenomenon also occurs in the [[Internet]]. Counting the number of links to a page can give us a general estimate of its prominence on the Web, but a page with very few incoming links may also be prominent, if two of these links come from the home pages of  [[Yahoo!]] or [[Google]] or [[MSN]]. Thus, because these sites are of very high importance but are also Search Engines, there can be very irrelevant results.


==Algorithm==
Cool temperament, short tail, face tough line in solemn time, that pious look, addition of a little quiet, the sin I look crazy.<br><br>mood always going to be destroyed, when Lin Yujing up, [http://www.dmwai.com/webalizer/kate-spade-6.html ケイトスペード バッグ 人気] that the monks in yellow again Jishou:. 'female donor, incense money three hundred.'<br><br>'ah!?' Lin Yujing moment, with the gas, but a look around the crowd strange eyes, she restrain down, dig a wallet, only to wrist was caught, it was sideways in front of him, is more than the crime, she thought To theory, and quickly pulled, for fear of a joke, but, [http://www.dmwai.com/webalizer/kate-spade-4.html ケイトスペード バッグ 新作] I can sin is very authentic with color harmonies Wyatt: 'Master, your spirit is [http://www.dmwai.com/webalizer/kate-spade-11.html ケイトスペードニューヨーク 財布] not working here, how money is not the first manifestation of the truth?'<br><br>'Xinchengzeling.' monk laughed, not resentful anger.<br><br>'is Xinchengzeling? still have money on the line?' I sin bared smiling.<br><br>old monk surprised a moment, laughed, like playing Eloquent general smiled and said:. 'willing to be money, Shi was the heart, so day Xinchengzeling'<br><br>'So, how much money [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペードのバッグ] is applied, but also a heart na.' sin than a [http://www.dmwai.com/webalizer/kate-spade-9.html バッグ ケイトスペード] smile
相关的主题文章：
<ul>
 
  <li>[http://www.wormwoodreview.com/cgi-bin/guestbook/guestbook.cgi http://www.wormwoodreview.com/cgi-bin/guestbook/guestbook.cgi]</li>
 
  <li>[http://www.health8.com/cgi-bin/yybbs/yybbs.cgi http://www.health8.com/cgi-bin/yybbs/yybbs.cgi]</li>
 
  <li>[http://www.ficoin.com/thread-31095-1-1.html http://www.ficoin.com/thread-31095-1-1.html]</li>
 
</ul>


In the HITS algorithm, the first step is to retrieve the most relevant pages to the search query. This set is called the ''root set'' and can be obtained by taking the top n pages returned by a text-based search algorithm. A ''base set'' is generated by augmenting the root set with all the web pages that are linked from it and some of the pages that link to it. The web pages in the base set and all hyperlinks among those pages form a focused subgraph. The HITS computation is performed only on this ''focused subgraph''. According to Kleinberg the reason for constructing a base set is to ensure that most (or many) of the strongest authorities are included.
== and I do not know what this old thief and a moth of. ==


Authority and hub values are defined in terms of one another in a [[mutual recursion]]. An authority value is computed as the sum of the scaled hub values that point to that page. A hub value is the sum of the scaled authority values of the pages it points to. Some implementations also consider the relevance of the linked pages.
Sin awe-inspiring, and I do not know what this old thief and a moth of.<br><br>At this time, the door photoacoustic big [http://www.dmwai.com/webalizer/kate-spade-12.html ケイトスペード ハンドバッグ] ring, 骆家龙 [http://www.dmwai.com/webalizer/kate-spade-6.html kate spade マザーズバッグ] and mouse Ben came in, pointing to the door and said: '? than children, dozens of SWAT teams to report the police cars ...... you'<br><br>than staring at the yellow crime Fenran liberation, stressing each syllable asked: '? You ... have surrendered.'<br><br>'yes ah, had surrendered to you can, but you do not accept.' Huang three smile.<br><br>'Truth is not what you got to hide.' I sin outraged, furious, he knew, into a public security door, there is no fear [http://www.dmwai.com/webalizer/kate-spade-10.html ケイトスペード 財布 セール] of his things.<br><br>'try, bad a dying old man, a city police to trace stolen property, who is the light who is heavy, I do not believe like [http://www.dmwai.com/webalizer/kate-spade-14.html ケイトスペード時計人気] you so take things too hard.' yellow three with a smile, as if he won a chip, and won The police seemed to [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード バッグ ショルダー] make him very happy with the general boasted: 'I am the master of fate or good, I do not like too much and you're so clever police deal with.'<br><br>'I'll check in the end of.' I sin a little gas with a hearing disorder
 
相关的主题文章：
The algorithm performs a series of iterations, each consisting of two basic steps:
  <ul>
*'''Authority Update''': Update each node's ''Authority score'' to be equal to the sum of the ''Hub Scores'' of each node that points to it. That is, a node is given a high authority score by being linked to by pages that are recognized as Hubs for information.
 
*'''Hub Update''': Update each node's ''Hub Score'' to be equal to the sum of the ''Authority Scores'' of each node that it points to. That is, a node is given a high hub score by linking to nodes that are considered to be authorities on the subject.
  <li>[http://www.yifangvisa.com/plus/feedback.php?aid=117 http://www.yifangvisa.com/plus/feedback.php?aid=117]</li>
 
 
The Hub score and Authority score for a node is calculated with the following algorithm:
  <li>[http://ladiesofthelake.com/cgi-bin/birthdaycard/guestbook.cgi http://ladiesofthelake.com/cgi-bin/birthdaycard/guestbook.cgi]</li>
* Start with each node having a hub score and authority score of 1.
    
* Run the Authority Update Rule
  <li>[http://www.shavahnchurch.com/cgi-bin/guestbook/guestbook.cgi http://www.shavahnchurch.com/cgi-bin/guestbook/guestbook.cgi]</li>
* Run the Hub Update Rule
 
* Normalize the values by dividing each Hub score by square root of the sum of the squares of all Hub scores, and dividing each Authority score by square root of the sum of the squares of all Authority scores.
</ul>
* Repeat from the second step as necessary.
 
HITS, like [[Larry Page|Page]] and [[Sergey Brin|Brin]]'s [[PageRank]], is an [[iterative algorithm]] based on the [[weblink|linkage of the documents on the web]]. However it does have some major differences:
* It is query dependent, that is, the (Hubs and Authority) scores resulting from the link analysis are influenced by the search terms;
* As a corollary, it is executed at query time, not at indexing time, with the associated hit on performance that accompanies query-time processing.
* It is not commonly used by search engines. (Though a similar algorithm was said to be used by [[Teoma]], which was acquired by [[Ask.com]].)
* It computes two scores per document, hub and authority, as opposed to a single score;
* It is processed on a small subset of ‘relevant’ documents (a 'focused subgraph' or base set), not all documents as was the case with PageRank.
 
== In detail ==
 
To begin the ranking, <math> \forall p </math>, <math>\mathrm{auth}(p) = 1</math> and <math>\mathrm{hub}(p) = 1</math>. We consider two types of updates: Authority Update Rule and Hub Update Rule. In order to calculate the hub/authority scores of each node, repeated iterations of the Authority Update Rule and the Hub Update Rule are applied. A k-step application of the Hub-Authority algorithm entails applying for k times first the Authority Update Rule and then the Hub Update Rule.
 
===Authority Update Rule===
 
<math>\forall p</math>, we update <math>\mathrm{auth}(p)</math> to be the summation:
 
<math>\mathrm{auth}(p)=\displaystyle\sum_{i=1}^n \mathrm{hub}(i)</math>
 
where n is the total number of pages connected to p and i is a page connected to p. That is, the Authority score of a page is the sum of all the Hub scores of pages that point to it.
 
===Hub Update Rule===
 
<math>\forall p</math>, we update <math>\mathrm{hub}(p)</math> to be the summation:
 
<math>\mathrm{hub}(p)=\displaystyle\sum_{i=1}^n \mathrm{auth}(i)</math>
 
where n is the total number of pages p connects to and i is a page which p connects to. Thus a page's Hub score is the sum of the Authority scores of all its linking pages
 
=== Normalization ===
The final hub-authority scores of nodes are determined after infinite repetitions of the algorithm. As directly and iteratively applying the Hub Update Rule and Authority Update Rule leads to diverging values, it is necessary to [[normalize]] the matrix after every iteration. Thus the values obtained from this process will eventually converge.<ref>{{cite web
  | last = von Ahn
  | first = Luis
  | authorlink = Luis von Ahn
  | coauthors =
  | title = Hubs and Authorities
  | work = 15-396: Science of the Web Course Notes
  | publisher = Carnegie Mellon University
  | date = 2008-10-19
  | url = http://www.scienceoftheweb.org/15-396/lectures/lecture13.pdf
  | format = PDF
  | doi =
  | accessdate = 2008-11-09}}</ref>
 
== Pseudocode ==
  1 ''G'' := set of pages
  2 '''for each''' page ''p'' in ''G'' '''do'''
  3  ''p''.auth = 1 // ''p''.auth is the authority score of the page ''p''
  4  ''p''.hub = 1 // ''p''.hub is the hub score of the page ''p''
  5 '''function''' HubsAndAuthorities(''G'')
  6  '''for''' step '''from''' 1 '''to''' k '''do''' // run the algorithm for k steps
  7    norm = 0
  8    '''for each''' page ''p'' in ''G'' '''do'''  // update all authority values first
  9      ''p''.auth = 0
10      '''for each''' page ''q'' in ''p.incomingNeighbors'' '''do''' // ''p.incomingNeighbors'' is the set of pages that link to ''p''
11          ''p''.auth += ''q''.hub
  12      norm += square(''p''.auth) // calculate the sum of the squared auth values to normalise
13    norm = sqrt(norm)
14    '''for each''' page ''p'' in ''G'' '''do'''  // update the auth scores
15      ''p''.auth = ''p''.auth / norm  // normalise the auth values
16    norm = 0
17    '''for each''' page ''p'' in ''G'' '''do'''  // then update all hub values
18      ''p''.hub = 0
19      '''for each''' page ''r'' in ''p.outgoingNeighbors'' '''do''' // ''p.outgoingNeighbors'' is the set of pages that ''p'' links to
20        ''p''.hub += ''r''.auth
21      norm += square(''p''.hub) // calculate the sum of the squared hub values to normalise
22    norm = sqrt(norm)
23    '''for each''' page ''p'' in ''G'' '''do'''  // then update all hub values
24      ''p''.hub = ''p''.hub / norm  // normalise the hub values
 
The hub and authority values converge in the pseudocode above.
 
The code below does not converge, because it is necessary to limit the number of steps that the algorithm runs for.  One way to get around this, however, would be to normalize the hub and authority values after each "step" by dividing each authority value by the square root of the sum of the squares of all authority values, and dividing each hub value by the square root of the sum of the squares of all hub values.  This is what the pseudocode above does.
 
== Non-converging pseudocode ==
  1 ''G'' := set of pages
  2 '''for each''' page ''p'' in ''G'' '''do'''
  3  ''p''.auth = 1 // ''p''.auth is the authority score of the page ''p''
  4  ''p''.hub = 1 // ''p''.hub is the hub score of the page ''p''
  5 '''function''' HubsAndAuthorities(''G'')
  6  '''for''' step '''from''' 1 '''to''' k '''do''' // run the algorithm for k steps
  7    '''for each''' page ''p'' in ''G'' '''do'''  // update all authority values first
   8      ''p''.auth = 0
  9      '''for each''' page ''q'' in ''p.incomingNeighbors'' '''do''' // ''p.incomingNeighbors'' is the set of pages that link to ''p''
10        ''p''.auth += ''q''.hub
11    '''for each''' page ''p'' in ''G'' '''do'''  // then update all hub values
12      ''p''.hub = 0
13      '''for each''' page ''r'' in ''p.outgoingNeighbors'' '''do''' // ''p.outgoingNeighbors'' is the set of pages that ''p'' links to
14        ''p''.hub += ''r''.auth
 
==References==
{{Reflist}}<!--added under references heading by script-assisted edit-->
*{{cite journal |last=Kleinberg |first=Jon |authorlink= |coauthors= |year=1999 |month= |title=Authoritative sources in a hyperlinked environment |journal=Journal of the ACM |volume=46 |issue=5 |pages=604–632 |id= |url=http://www.cs.cornell.edu/home/kleinber/auth.pdf |format=PDF|accessdate= |quote= |doi=10.1145/324133.324140 }}
*{{cite book |chapter=Improvement of HITS-based Algorithms on Web Documents |title=Proceedings of the 11th International World Wide Web Conference (WWW 2002) |last=Li |first=L. |authorlink= |coauthors=Shang, Y.; Zhang, W. |year=2002 |publisher= |location=Honolulu, HI |isbn=1-880672-20-0 |pages= |chapterurl=http://www2002.org/CDROM/refereed/643/ }}
 
==External links==
*{{US patent|6112202}}
*[http://www.dupuis.me/node/25 Create a data search engine from a relational database] Search engine in C# based on HITS
 
[[Category:Link analysis]]

Latest revision as of 23:23, 9 October 2014

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The level is also able to push on the push, their hearts more clearly, the kind of people who commit crimes than their whatever, ケイトスペード マザーズバッグ but like this mimicking 'whoring' was ripped off, and would not give sympathy and concern, at most, give evaluation : deserve.

'head back ...... there is a second case in return?' I asked the crime.

'Yes, I went to the police station, they gave me one who sinks the 80,000 special smile stomach ache ...... what drops, do not laugh at me silly chant, and later gave registered under, let me come back to other news , First Nima did not sound a. 'big golden bowl depressed authentic.

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'I will not do anything ......

, Also boast Xiong Jianfei lot, boast not know exactly how everyone was a different story.

Implying really struggling to find a police force, we are qualified?

wrong, there is one more than the crime, this time only to find 许平秋 is skipped over sin praise of others, finished just turned around and asked more than crime, ケイトスペード 財布 通販 very puzzled and asked the remainder of ケイトスペードニューヨーク 財布 sin and said: 'I sin, what are you doing up how the family did not get you? too much information. '

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. 'willing to be money

Cool temperament, short tail, face tough line in solemn time, that pious look, addition of a little quiet, the sin I look crazy.

mood always going to be destroyed, when Lin Yujing up, ケイトスペード バッグ 人気 that the monks in yellow again Jishou:. 'female donor, incense money three hundred.'

'ah!?' Lin Yujing moment, with the gas, but a look around the crowd strange eyes, she restrain down, dig a wallet, only to wrist was caught, it was sideways in front of him, is more than the crime, she thought To theory, and quickly pulled, for fear of a joke, but, ケイトスペード バッグ 新作 I can sin is very authentic with color harmonies Wyatt: 'Master, your spirit is ケイトスペードニューヨーク 財布 not working here, how money is not the first manifestation of the truth?'

'Xinchengzeling.' monk laughed, not resentful anger.

'is Xinchengzeling? still have money on the line?' I sin bared smiling.

old monk surprised a moment, laughed, like playing Eloquent general smiled and said:. 'willing to be money, Shi was the heart, so day Xinchengzeling'

'So, how much money ケイトスペードのバッグ is applied, but also a heart na.' sin than a バッグ ケイトスペード smile 相关的主题文章：

and I do not know what this old thief and a moth of.

Sin awe-inspiring, and I do not know what this old thief and a moth of.

At this time, the door photoacoustic big ケイトスペード ハンドバッグ ring, 骆家龙 kate spade マザーズバッグ and mouse Ben came in, pointing to the door and said: '? than children, dozens of SWAT teams to report the police cars ...... you'

than staring at the yellow crime Fenran liberation, stressing each syllable asked: '? You ... have surrendered.'

'yes ah, had surrendered to you can, but you do not accept.' Huang three smile.

'Truth is not what you got to hide.' I sin outraged, furious, he knew, into a public security door, there is no fear ケイトスペード 財布 セール of his things.

'try, bad a dying old man, a city police to trace stolen property, who is the light who is heavy, I do not believe like ケイトスペード時計人気 you so take things too hard.' yellow three with a smile, as if he won a chip, and won The police seemed to ケイトスペード バッグ ショルダー make him very happy with the general boasted: 'I am the master of fate or good, I do not like too much and you're so clever police deal with.'

'I'll check in the end of.' I sin a little gas with a hearing disorder 相关的主题文章：

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