2013-01-24 18:50:05 +01:00
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\subsection{Idea}
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\begin{frame}{The early days}
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\begin{itemize}[<+->]
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\item Humans know what is good for them
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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 numbers of Websites that link to a Website
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\item[\xmark] Quality of the page 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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2013-01-24 19:34:42 +01:00
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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{$page \in G$}
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\alertline<3> \State $page.pageRank = \frac{1}{|G|}$ \Comment{intial probability}
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\alertline<2> \EndFor
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\alertline<4> \While{$iterations > 0$}
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\alertline<5> \ForAll{$page \in G$} \Comment{calculate pageRank of $page$}
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\alertline<6> \State $page.pageRank = q$
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\alertline<7> \ForAll{$y \in L(page)$}
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\alertline<8> \State $page.pageRank$ += $\frac{y.pageRank}{C(y)}$
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\alertline<7> \EndFor
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\alertline<5> \EndFor
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\alertline<4> \State $iterations$ -= $1$
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\alertline<4> \EndWhile
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\alertline<1> \EndFunction
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\end{algorithmic}
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\end{frame}
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