From 899cd5afe2ff6c0efaa7c26170943ab956669405 Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sun, 12 Jan 2014 17:20:36 +0100 Subject: [PATCH] =?UTF-8?q?starke=20=C3=9Cberarbeitung?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- documents/DYCOS/DYCOS-Algorithmus.tex | 105 +++++++++---------- documents/DYCOS/DYCOS.pdf | Bin 470766 -> 473563 bytes documents/DYCOS/DYCOS.tex | 1 + documents/DYCOS/SchwaechenVerbesserungen.tex | 37 ++++--- documents/DYCOS/Sprungtypen.tex | 2 +- documents/DYCOS/Vokabularbestimmung.tex | 8 +- documents/DYCOS/figures/graph-t2.tex | 2 +- documents/DYCOS/figures/graph-t3.tex | 4 +- documents/DYCOS/figures/graph-t4.tex | 15 +++ 9 files changed, 97 insertions(+), 77 deletions(-) create mode 100644 documents/DYCOS/figures/graph-t4.tex diff --git a/documents/DYCOS/DYCOS-Algorithmus.tex b/documents/DYCOS/DYCOS-Algorithmus.tex index 56c7d2d..4ca83d3 100644 --- a/documents/DYCOS/DYCOS-Algorithmus.tex +++ b/documents/DYCOS/DYCOS-Algorithmus.tex @@ -2,18 +2,15 @@ DYCOS (\underline{DY}namic \underline{C}lassification algorithm with c\underline{O}ntent and \underline{S}tructure) ist ein Knotenklassifizierungsalgorithmus, der Ursprünglich in \cite{aggarwal2011} vorgestellt -wurde. Er klassifiziert Knoten, indem mehrfach Random Walks startend -bei dem zu klassifizierenden Knoten $v$ gemacht werden und die Labels -der besuchten Knoten gezählt werden. Das Label, das am häufigsten +wurde. Er klassifiziert einzelne Knoten, indem $r$ Random Walks der Länge $l$, +startend bei dem zu klassifizierenden Knoten $v$ gemacht werden. Dabei +werden die Labels der besuchten Knoten gezählt. Das Label, das am häufigsten vorgekommen ist, wird als Label für $v$ gewählt. DYCOS nutzt also die sog. Homophilie, d.~h. die Eigenschaft, dass Knoten, die nur wenige Hops von einander entfernt sind, häufig auch -ähnlich sind \cite{bhagat}. - -Der DYCOS-Algorithmus nimmt jedoch nicht einfach den Graphen für -dieses Verfahren, sondern erweitert ihn mit Hilfe der zur Verfügung -stehenden Texte. - +ähnlich sind \cite{bhagat}. Der DYCOS-Algorithmus nimmt jedoch nicht +einfach den Graphen für dieses Verfahren, sondern erweitert ihn mit +Hilfe der zur Verfügung stehenden Texte.\\ Für diese Erweiterung wird zuerst wird Vokabular $W_t$ bestimmt, das charakteristisch für eine Knotengruppe ist. Wie das gemacht werden kann und warum nicht einfach jedes Wort in das Vokabular aufgenommen wird, @@ -24,6 +21,12 @@ Knoten, die der Graph zuvor hatte, werden nun \enquote{Strukturknoten} genannt. Ein Strukturknoten $v$ wird genau dann mit einem Wortknoten $w \in W_t$ verbunden, wenn $w$ in einem Text von $v$ vorkommt. +Der DYCOS-Algorithmus betrachtet also die Texte, die einem Knoten +zugeornet sind, als eine Multimenge von Wörtern. Das heißt, zum einen +wird nicht auf die Reihenfolge der Wörter geachtet, zum anderen wird +bei Texten eines Knotens nicht zwischen verschiedenen +Texten unterschieden. Jedoch wird die Anzahl der Vorkommen +jedes Wortes berücksichtigt. \begin{figure}[htp] \centering @@ -43,10 +46,9 @@ die strukturellen Sprünge und inhaltliche Mehrfachsprünge: Knoten $v \in V_t$ zu einem benachbartem Knoten $w \in V_t$ ein \textbf{struktureller Sprung}. \end{definition} - +\goodbreak Im Gegensatz dazu benutzten inhaltliche Mehrfachsprünge tatsächlich die Grapherweiterung: - \begin{definition} Sei $G_t = (V_t, E_{S,t} \cup E_{W,t}, V_{L,t}, W_{t})$ der um die Wortknoten $W_{t}$ erweiterte Graph. @@ -60,46 +62,13 @@ tatsächlich die Grapherweiterung: Jeder inhaltliche Mehrfachsprung beginnt und endet also in einem Strukturknoten, springt über einen Wortknoten und ist ein Pfad der Länge~2. -Bevor der DYCOS-Algorithmus im Detail erklärt wird, sei noch auf eine -Besonderheit hingewiesen: -Der DYCOS-Algorithmus betrachtet die Texte, die einem Knoten -zugeornet sind, als eine Multimenge von Wörtern. Das heißt, zum einen -wird nicht auf die Reihenfolge der Wörter geachtet, zum anderen wird -bei Texten eines Knotens nicht zwischen verschiedenen -Texten unterschieden. Jedoch wird die Anzahl der Vorkommen -jedes Wortes berücksichtigt. - -\subsection{Datenstrukturen} -Zusätzlich zu dem gerichteten Graphen $G_t = (V_t, E_t, V_{L,t})$ -verwaltet der DYCOS-Algorithmus zwei weitere Datenstrukturen: -\begin{itemize} - \item Für jeden Knoten $v \in V_t$ werden die vorkommenden Wörter, - die auch im Vokabular $W_t$ sind, - und deren Anzahl gespeichert. Das könnte z.~B. über ein - assoziatives Array geschehen. Wörter, die nicht in - Texten von $v$ vorkommen, sind nicht im Array. Für - alle vorkommenden Wörter ist der gespeicherte Wert zum - Schlüssel \enquote{Wort} die Anzahl der Vorkommen von - \enquote{Wort} in den Texten von $v$. - \item Für jedes Wort des Vokabulars $W_t$ wird eine Liste von - Knoten verwaltet, in deren Texten das Wort vorkommt. - \item An einigen Stellen macht ein assoziatives Array, auch - \enquote{dictionary} oder \enquote{map} genannt, sinn. - Zustätzlich ist es nützlich, wenn diese Datenstruktur für - unbekannte Schlüssel keinen Fehler ausgibt, sondern für diese - Schlüssel den Wert 0 annimmt. Eine solche Datenstruktur - wird in Python \texttt{defaultdict} genannt und ich werde - im Folgenden diese Benennung beibehalten. -\end{itemize} - -\input{Sprungtypen} -\input{Vokabularbestimmung} - -\subsection{Der Algorithmus} -Der DYCOS-Algorithmus verwendet nun für jeden Knoten der gelabelt wird -$r$ Random Walks der Länge $l$, wobei mit einer Wahrscheinlichkeit -$p_S$ ein struktureller Sprung und mit einer Wahrscheinlichkeit -von $(1-p_S)$ ein inhaltlicher Mehrfachsprung gemacht wird. Dieser +Ob in einem Sprung der Random Walks ein struktureller Sprung oder +ein inhaltlicher Mehrfachsprung gemacht wird, wird jedes mal zufällig +neu entschiden. Dafür wird der Parameter $0 \leq p_S \leq 1$ für den Algorithmus +gewählt. Mit einer Wahrscheinlichkeit von $p_S$ wird eine struktureller +Sprung durchgefürt und mit einer Wahrscheinlichkeit +von $(1-p_S)$ ein modifizierter inhaltlicher Mehrfachsprung, wie er in +\cref{sec:sprungtypen} erklärt wird, gemacht. Dieser Parameter gibt an, wie wichtig die Struktur des Graphen im Verhältnis zu den textuellen Inhalten ist. Bei $p_S = 0$ werden ausschließlich die Texte betrachtet, bei $p_S = 1$ ausschließlich die Struktur des @@ -108,14 +77,12 @@ Graphen. Die Vokabularbestimmung kann zu jedem Zeitpunkt $t$ durchgeführt werden, muss es aber nicht. -In \cref{alg:DYCOS} wurde der DYCOS-Algorithmus als -Pseudocode vorgestellt. Dafür werden die beiden Hilfsfunktionen -für den strukturellen Sprung sowie den inhaltlichen Mehrfachsprung -benötigt. +In \cref{alg:DYCOS} wird der DYCOS-Algorithmus als +Pseudocode vorgestellt. \begin{algorithm} \begin{algorithmic}[1] - \Require \\$G_t = (V_t, E_t, V_{L,t})$ (Netzwerk),\\ + \Require \\$G_{E,t} = (V_t, E_{S,t} \cup E_{W,t}, V_{L,t}, W_t)$ (Erweiterter Graph),\\ $r$ (Anzahl der Random Walks),\\ $l$ (Länge eines Random Walks),\\ $p_s$ (Wahrscheinlichkeit eines strukturellen Sprungs),\\ @@ -154,3 +121,29 @@ benötigt. \caption{DYCOS-Algorithmus} \label{alg:DYCOS} \end{algorithm} + +\subsection{Datenstrukturen} +Zusätzlich zu dem gerichteten Graphen $G_t = (V_t, E_t, V_{L,t})$ +verwaltet der DYCOS-Algorithmus zwei weitere Datenstrukturen: +\begin{itemize} + \item Für jeden Knoten $v \in V_t$ werden die vorkommenden Wörter, + die auch im Vokabular $W_t$ sind, + und deren Anzahl gespeichert. Das könnte z.~B. über ein + assoziatives Array geschehen. Wörter, die nicht in + Texten von $v$ vorkommen, sind nicht im Array. Für + alle vorkommenden Wörter ist der gespeicherte Wert zum + Schlüssel \enquote{Wort} die Anzahl der Vorkommen von + \enquote{Wort} in den Texten von $v$. + \item Für jedes Wort des Vokabulars $W_t$ wird eine Liste von + Knoten verwaltet, in deren Texten das Wort vorkommt. + \item An einigen Stellen macht ein assoziatives Array, auch + \enquote{dictionary} oder \enquote{map} genannt, sinn. + Zustätzlich ist es nützlich, wenn diese Datenstruktur für + unbekannte Schlüssel keinen Fehler ausgibt, sondern für diese + Schlüssel den Wert 0 annimmt. Eine solche Datenstruktur + wird in Python \texttt{defaultdict} genannt und ich werde + im Folgenden diese Benennung beibehalten. +\end{itemize} + +\input{Sprungtypen} +\input{Vokabularbestimmung} diff --git a/documents/DYCOS/DYCOS.pdf b/documents/DYCOS/DYCOS.pdf index e4aadd9df5f75c78adcabd97535c3423f8bdef97..e0e8b481e0710088e8ad7ab827f89664799740fd 100644 GIT binary patch delta 152145 zcmZs?LwGI<(4`yOwrxAvv2EM7lP}t_Z6`anZQHhOs73QP#}f!qt+9g`JB#sh^3e zaSyZ>8eru^tQ=+`DOdxnRufO5LS+~yDAVGK(&rm(k2Ir|7-0W zshSz_kQkEGbug+zwryNH%eDCJAxnP1P(SC~)rF{X6E@SZ- z3}IFs=?w^bVAIyS(WT*v^@Bc)RtXZ_Q=JS(&-rPueTYtUfOZg{KW#qN)4eR=YN!-e zYVk#q#kd>`(?Q^V#X5u4ql-~wZt-V#Fo$?)w?2X$MX2FsWc1^vP?pp5tbGi1<}`4O zpn@fZH7Mvz)eEtn5?SS5^58uwPJ=kOfTkJ-7bwK8f4p=xCx1~`Z5pKagA0@MV`6UA zK+>?bpCD(=uemLWuG=buP;o|9fMA5Q3cx6na(S z{Rr`3Jzd={owlM%&d{E=|%WF>$7Jy<@m-fjN&j!G_?4b$t~hCns?*fnqV zD9@k;tb?b-It-YueVLU_|D_SDV9oA2Pvu0Yb3AZ~Y1=rN!?XPQ>`GM}OPh2%4GL-k 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(c)[vertex,label=$B$] at (2,0) {$v_3$}; - \draw[->] (a) -- (b); - \draw[->] (c) -- (b); + \draw[->] (b) -- (a); + \draw[->] (b) -- (c); \node (struktur)[label={[label distance=-0.2cm]0:$t=3$}] at (-1,1) {}; \end{tikzpicture} diff --git a/documents/DYCOS/figures/graph-t4.tex b/documents/DYCOS/figures/graph-t4.tex new file mode 100644 index 0000000..6b217c6 --- /dev/null +++ b/documents/DYCOS/figures/graph-t4.tex @@ -0,0 +1,15 @@ +\tikzstyle{vertex}=[draw,black,circle,minimum size=10pt,inner sep=0pt] +\tikzstyle{edge}=[very thick] +\begin{tikzpicture}[scale=1,framed] + \node (a)[vertex,label=$A$] at (0,0) {$v_1$}; + \node (b)[vertex,label=45:{\color{blue}$A$}] at (1,0) {$v_2$}; + \node (c)[vertex,label=$B$] at (2,0) {$v_3$}; + \node (d)[vertex] at (1,1) {$v_4$}; + \draw[->] (b) -- (a); + \draw[->] (b) -- (c); + + \draw[->] (d) -- (a); + \draw[->] (d) -- (b); + \draw[->] (d) -- (c); + \node (struktur)[label={[label distance=-0.2cm]0:$t=3$}] at (-1,1) {}; +\end{tikzpicture}