From 403fa74df95dab204917103edfe5cca7e57c6245 Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sat, 11 Jan 2014 19:27:50 +0100 Subject: [PATCH] =?UTF-8?q?TODOs=20entfernt;=20Abschnitt=20'Schw=C3=A4chen?= =?UTF-8?q?'=20hinzugef=C3=BCgt;=20Nun=20wird=20nur=20noch=20der=20DYCOS-A?= =?UTF-8?q?lgorithmus=20aus=20dem=20Paper=20beschrieben;=20Struktur=20ver?= =?UTF-8?q?=C3=A4ndert;=20Abschnitt=20=C3=BCber=20Analyse=20entfernt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- documents/DYCOS/Abgrenzung.tex | 2 +- documents/DYCOS/Ausblick.tex | 6 +- documents/DYCOS/DYCOS-Algorithmus.tex | 154 +++++++++---------- documents/DYCOS/DYCOS.pdf | Bin 403059 -> 465806 bytes documents/DYCOS/DYCOS.tex | 17 +- documents/DYCOS/Einleitung.tex | 10 +- documents/DYCOS/README.md | 4 + documents/DYCOS/SchwaechenVerbesserungen.tex | 89 +++++++++++ documents/DYCOS/Sprungtypen.tex | 87 +++++++++++ documents/DYCOS/Vokabularbestimmung.tex | 7 +- documents/DYCOS/abstract.tex | 7 +- documents/DYCOS/literatur.bib | 43 ++++++ 12 files changed, 319 insertions(+), 107 deletions(-) create mode 100644 documents/DYCOS/README.md create mode 100644 documents/DYCOS/SchwaechenVerbesserungen.tex create mode 100644 documents/DYCOS/Sprungtypen.tex diff --git a/documents/DYCOS/Abgrenzung.tex b/documents/DYCOS/Abgrenzung.tex index 16aaf7b..36986c6 100644 --- a/documents/DYCOS/Abgrenzung.tex +++ b/documents/DYCOS/Abgrenzung.tex @@ -1,4 +1,4 @@ -Der in diesem Artikel vorgestellte DYCOS-Algorithmus wurde 2011 von +Der in dieser Ausarbeitung vorgestellte DYCOS-Algorithmus wurde 2011 von Charu~C. Aggarwal und Nan~Li in \cite{aggarwal2011} vorgestellt. Es gibt jedoch viele Klassifizierungsalgorithmen, die ähnliche Ideen nutzen. Einige dieser Algorithmen werden im Folgenden kurz vorgestellt diff --git a/documents/DYCOS/Ausblick.tex b/documents/DYCOS/Ausblick.tex index cd3b14a..35968f8 100644 --- a/documents/DYCOS/Ausblick.tex +++ b/documents/DYCOS/Ausblick.tex @@ -1,13 +1,13 @@ Den sehr einfach aufgebauten DYCOS-Algorithmus kann man noch an vielen Punkten verbessern. So könnte man vor der Auswahl des Vokabulars jedes Wort auf den Wortstamm zurückführen. -Dafür könnte zum Beispiel der \todo{Wo steht was über den?}{Porter-Stemming-Algorithmus} verwendet -werden. Durch diese Maßnahme wird das +Dafür könnte zum Beispiel der Porter-Stemming-Algorithmus verwendet +werden \cite{porter}. Durch diese Maßnahme wird das Vokabular kleiner gehalten, mehr Artikel können mit einander durch Vokabular verbunden werden und der Gini-Koeffizient wird ein besseres Maß für die Gleichheit von Texten. -Eine weitere Verbesserungsmöglichkeit besteht in der textanalyse. +Eine weitere Verbesserungsmöglichkeit besteht in der Textanalyse. Momentan ist diese noch sehr einfach gestrickt und ignoriert die Reihenfolge von Wortern beziehungsweise Wertungen davon. So könnte man den DYCOS-Algorithmus in einem sozialem Netzwerk verwenden wollen, diff --git a/documents/DYCOS/DYCOS-Algorithmus.tex b/documents/DYCOS/DYCOS-Algorithmus.tex index e9e2cb9..8d58919 100644 --- a/documents/DYCOS/DYCOS-Algorithmus.tex +++ b/documents/DYCOS/DYCOS-Algorithmus.tex @@ -5,7 +5,11 @@ Knotenklassifizierungsalgorithmus, der Ursprünglich in \cite{aggarwal2011} vorg wurde. Er klassifiziert Knoten, indem mehrfach Random Walks startend bei dem zu klassifizierenden Knoten gemacht werden und die Labels der besuchten Knoten gezählt werden. Das Label, das am häufigsten -vorgekommen ist, wird zur Klassifizierung verwendet. +vorgekommen ist, wird als Label 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. @@ -28,6 +32,32 @@ verbunden, wenn $w$ in einem Text von $v$ vorkommt. \label{fig:erweiterter-graph} \end{figure} +Entsprechend werden zwei unterschiedliche Sprungtypen unterschieden, +die strukturellen Sprünge und inhaltliche Mehrfachsprünge: + +\begin{definition} + Sei $G_{E,t} = (V_t, E_{S,t} \cup E_{W,t}, V_{L,t}, W_{t})$ der + um die Wortknoten $W_{t}$ erweiterte Graph. + + Dann heißt das zufällige wechseln des aktuell betrachteten + Knoten $v \in V_t$ zu einem benachbartem Knoten $w \in V_t$ + ein \textbf{struktureller Sprung}. +\end{definition} + +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. + + Dann heißt das zufällige wechseln des aktuell betrachteten + Knoten $v \in V_t$ zu einem benachbartem Knoten $w \in W_t$ + und weiter zu Nachbar von $v' \in V_t$ von $w$ + ein \textbf{inhaltlicher Mehrfachsprung}. $v'$ ist also genau + einen Sprung über einen Wortknoten $w$ von $v$ entfernt. +\end{definition} + Der DYCOS-Algorithmus betrachtet die Texte, die einem Knoten zugeornet sind, als eine Multimenge von Wörtern. Das heißt, zum einen wird nicht auf die @@ -49,111 +79,69 @@ verwaltet der DYCOS-Algorithmus zwei weitere Datenstrukturen: \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} -\subsection{Algorithmen} -Bevor der Algorithmus formal beschrieben wird, wird eine Definition -des strukturellen $l$-Sprungs benötigt: -\begin{definition} - Sei $G_{E,t} = (V_t, E_{S,t} \cup E_{W,t}, V_{L,t}, W_{t})$ der - um die Wortknoten $W_{t}$ erweiterte Graph. +\input{Sprungtypen} +\input{Vokabularbestimmung} - Dann heißt ein Random Walk der Länge $l$ in diesem Graphen - ein \textbf{struktureller $l$-Sprung}, wenn für den Random Walk - nur Kanten aus $E_{S,t}$ benutzt werden. -\end{definition} +\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 $l$-Sprung und mit einer Wahrscheinlichkeit +von $(1-p_S)$ ein inhaltlicher $l$-Mehrfachsprung gemacht wird. -Der strukturelle $l$-Sprung ist also ein Random Walk der Länge $l$ -im Graph $G_t$. Im Gegensatz dazu benötigt der inhaltliche $l$-Mehrfachsprung -tatsächlich die Grapherweiterung: +Die Vokabularbestimmung kann zu jedem Zeitpunkt $t$ durchgeführt +werden, muss es aber nicht. -\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. - - Dann heißt ein Random Walk der Länge $l$ in diesem Graphen - ein \textbf{inhaltlicher $l$-Mehrfachsprung}, wenn für den Random Walk - in jedem der $l$ Schritte, startend von einem Knoten $v \in V_t$ - eine Kante zu einem Wortknoten und von dem Wortknoten wieder - zu einem Strukturknoten genommen wird. -\end{definition} +Im Folgenden werde ich den DYCOS-Algorithmus als Pseudocode vorstellen. +Dafür benötigt man die beiden Hilfsfunktionen für den strukturellen +Sprung sowie den inhaltlichen Mehrfachsprung: \begin{algorithm}[H] - \begin{algorithmic} + \begin{algorithmic}[1] \Require \\$\G_t = (\N_t, \A_t, \T_t)$ (Netzwerk),\\ $r$ (Anzahl der Random Walks),\\ $l$ (Länge eines Random Walks),\\ - $p_s$ (Wahrscheinlichkeit eines strukturellen Sprungs) + $p_s$ (Wahrscheinlichkeit eines strukturellen Sprungs),\\ + $q$ (Anzahl der betrachteten Knoten nach der Aggregatanalyse) \Ensure Klassifikation von $\N_t \setminus \T_t$\\ - - \Procedure{SturkturellerSprung}{Dictionary $d$, Startknoten $v$, Länge $l$} - \For{$i$ von $1$ bis $l$} - \State $v \gets v.\Call{Next}{}$ - \ForAll{Label $w$ in v.\Call{GetLabels}{}} - \State $d[w] = d[w] + 1$ - \EndFor - \EndFor - \EndProcedure - \\ - \Procedure{InhaltlicherMehrfachsprung}{Dictionary $d$, Startknoten $v$, Länge $l$} - \For{$i$ von $1$ bis $l$} - \State $v \gets v.\Call{Next}{}$ \Comment{TODO: Hier muss ein mehrfachsprung beschrieben werden!} - \ForAll{Label $w$ in v.\Call{GetLabels}{}} - \State $d[w] = d[w] + 1$ - \EndFor - \EndFor - \EndProcedure \\ \ForAll{Knoten $v$ in $\N_t \setminus \T_t$} - \State $d \gets $ Dictionary, das für neue Einträge 0 annimmt + \State $d \gets $ defaultdict \For{$i$ von $1$ bis $r$} - \State $sprungTyp \gets \Call{random}{0, 1}$ - \If{$sprungTyp \leq p_S$} - \State \Call{SturkturellerSprung}{$v$, $l$} - \Else - \State \Call{InhaltlicherMehrfachsprung}{$v$, $l$} - \EndIf + \State $w \gets v$ + \For{$j$ von $1$ bis $l$} + \State $sprungTyp \gets \Call{random}{0, 1}$ + \If{$sprungTyp \leq p_S$} + \State $w \gets$ \Call{SturkturellerSprung}{$w$} + \Else + \State $w \gets$ \Call{InhaltlicherMehrfachsprung}{$w$} + \EndIf + \State $w \gets v.\Call{GetLabel}{ }$ \Comment{Zähle das Label} + \State $d[w] \gets d[w] + 1$ + \EndFor \EndFor - \If{$d$ ist leer} - \State $M_H \gets \Call{HäufigsteLabelImGraph}{}$ - \ForAll{$label$ in $M_H$} - \State $v.\Call{AddLabel}{label}$ - \EndFor + \If{$d$ ist leer} \Comment{Es wurde kein gelabelter Knoten gesehen} + \State $M_H \gets \Call{HäufigsteLabelImGraph}{ }$ \Else \State $M_H \gets \Call{max}{d}$ - \ForAll{$label$ in $M_H$} - \State $v.\Call{AddLabel}{label}$ - \EndFor \EndIf + \\ + \State \Comment{Wähle aus der Menge der häufigsten Label $M_H$ zufällig eines aus} + \State $label \gets \Call{Random}{M_H}$ + \State $v.\Call{AddLabel}{label}$ \Comment{und weise dieses $v$ zu} \EndFor \State \Return Labels für $\N_t \setminus \T_t$ \end{algorithmic} \caption{DYCOS-Algorithmus} \label{alg:DYCOS} \end{algorithm} - -\subsection{Inhaltliche Mehrfachsprünge} -Es ist nicht sinnvoll, direkt von einem strukturellem Knoten -$v \in \N_t$ zu einem mit $v$ verbundenen Wortknoten $w$ zu springen -und von diesem wieder zu einem verbundenem strutkurellem Knoten -$v' \in \N_t$. Würde man dies machen, wäre zu befürchten, dass -aufgrund von Homonymen die Qualität der Klassifizierung verringert -wird. So hat \enquote{Brücke} im Deutschen viele Bedeutungen. -Gemeint sein können z.~B. das Bauwerk, das Entwurfsmuster der -objektorientierten Programmierung oder ein Teil des Gehirns. - -Deshalb wird für jeden Knoten $v$, von dem aus man einen inhaltlichen -Mehrfachsprung machen will folgendes vorgehen gewählt: -\begin{enumerate} - \item Gehe alle in $v$ startenden Random Walks der Länge 2 durch - und erstelle eine Liste $L$, der erreichbaren Knoten $v'$. Speichere - außerdem, durch wie viele Pfade diese Knoten $v'$ jeweils erreichbar sind. - \item Betrachte im folgenden nur die Top-$q$ Knoten, wobei $q \in \mathbb{N}$ - eine zu wählende Konstante des Algorithmus ist. - \item Wähle mit Wahrscheinlichkeit $\frac{\Call{Anzahl}{v'}}{\sum_{w \in L} \Call{Anzahl}{v'}}$ - den Knoten $v'$ als Ziel des Mehrfachsprungs. -\end{enumerate} - -\input{Vokabularbestimmung} diff --git a/documents/DYCOS/DYCOS.pdf b/documents/DYCOS/DYCOS.pdf index 3c1827f0c5ddf06dfd9045394797f29a3e4bcaaa..91bd02655eaafb7f29b38ca4bf5d59632c471183 100644 GIT binary patch delta 340861 zcmZs>V{o8d)UFxZwrzK8+v(W0ohP=fj%}l3cWm1o+vs_}GgGH#YRMhY_YmrX$*tTO;O8~S(%$UhAf?i_=WwWzFq3Vzft-$ zm`JTkCuyv(H9V3c3{QXdc#9Moe-39nz>I3MX-zHG2mIbXu`L98(s6WDXa$gJt#Ku+ zT~J+-ZJfMv+`OEAW!J3yOHvU40q~~rmbG6Qz&Dfc1)AtqfJ&F{j?M4$r9unSH+7CIPzIa z3Voi_*hbx_K?cEO`Puv85B zyN(;aDP=;hPf&y)O(4oTT)=(+E!0Jb#Y7y%N48t*^Sp&zi7q2=fyxzu;!r zo3r?z1IyFJCJEUy3@A53Q*uz6i>UO13nILUB4Gx2ApFhZp%)EfZ&`E!7V?2es?MZl 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