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108 lines
4.1 KiB
TeX
108 lines
4.1 KiB
TeX
\subsection{How can we use this massive amout of information?}
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\begin{frame}{How can we use this massive amout of information?}
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\begin{itemize}[<+->]
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\item 625.3 million websites
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\item Wikipedia is one website and has several millions of pages
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\item[$\Rightarrow$] we need to rank websites!
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\end{itemize}
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\end{frame}
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\subsection{Idea}
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\begin{frame}{Basics of PageRank}
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We all know that:
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\begin{itemize}[<+->]
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\item humans know what is good for them
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\item[\xmark] machines don't know what's good for humans
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\item humans create websites
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\item humans will only \href{http://en.wikipedia.org/wiki/Hyperlink}{link} to websites they like
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\item[$\Rightarrow$] hyperlinks are a quality indicator
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\end{itemize}
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\end{frame}
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\begin{frame}{How Could We Use That?}
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\begin{itemize}[<+->]
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\item simply count number of links to a website
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\item[\xmark] 10,000 links from only one page
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\item count number of websites that link to a website
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\item[\xmark] quality of the linking website matters
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\item[\xmark] total number of links on the source page matters
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\end{itemize}
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\end{frame}
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\framedgraphic{A Brilliant Idea}{../images/BrinPage.jpg}
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\begin{frame}{Ideas of PageRank}
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\begin{itemize}[<+->]
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\item decisions of humans are complicated
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\item a lot of webpages get visited
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\item[$\Rightarrow$] modellize clicks on links as random behaviour
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\item links are important
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\begin{itemize}
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\item links of page A get less important, if A has many links
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\item links of page A get more important, if many link to A
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\end{itemize}
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\item[$\Rightarrow$] if B has a link from A, the rank of B increases by $\frac{Rank(A)}{Links(A)}$
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\end{itemize}
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\pause[\thebeamerpauses]
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\begin{algorithmic}
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\If{A links to B}
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\State $Rank(B)$ += $\frac{Rank(A)}{Links(A)}$
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\EndIf
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\end{algorithmic}
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\end{frame}
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\begin{frame}{What is PageRank?}
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The PageRank algorithm calculates the probability of a randomly
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clicking user ending up on a given page.
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\end{frame}
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\input{Animation}
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%\begin{frame}{Ants}
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% \begin{itemize}[<+->]
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% \item Websites = nodes = anthill
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% \item Links = edges = paths
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% \item You place ants on each node
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% \item They walk over the paths
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% \item[] (at random, they are ants!)
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% \item After some time, some anthills will have more ants than
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% others
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% \item Those hills are more attractive than others
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% \item \# ants is probability that a random user would end on
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% a website
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% \end{itemize}
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%\end{frame}
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\begin{frame}{Mathematics}
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Let $x$ be a web page. Then
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\begin{itemize}
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\item $L(x)$ is the set of websites that link to $x$
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\item $C(y)$ is the out-degree of page $y$
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\item $\alpha$ is probability of random jump
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\item $N$ is the total number of websites
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\end{itemize}
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\[\displaystyle PR(x) := \alpha \left ( \frac{1}{N} \right ) + (1-\alpha) \sum_{y\in L(x)} \frac{PR(y)}{C(y)}\]
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\end{frame}
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\begin{frame}{Pseudocode}
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\begin{algorithmic}
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\alertline<1> \Function{PageRank}{Graph $web$, double $q=0.15$, int $iterations$} %q is a damping factor
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%\alertline<2> \ForAll{$page \in web$}
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%\alertline<3> \State $page.pageRank = \frac{1}{|web|}$ \Comment{intial probability}
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%\alertline<2> \EndFor
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\alertline<2> \While{$iterations > 0$}
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\alertline<3> \ForAll{$page \in web$} \Comment{calculate pageRank of $page$}
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\alertline<4> \State $page.pageRank = q$
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\alertline<5> \ForAll{$y \in L(page)$}
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\alertline<6> \State $page.pageRank$ += $\frac{y.pageRank}{C(y)}$
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\alertline<5> \EndFor
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\alertline<3> \EndFor
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\alertline<2> \State $iterations$ -= $1$
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\alertline<2> \EndWhile
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\alertline<1> \EndFunction
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\end{algorithmic}
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\end{frame}
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