Final version for mini project - just cutting our losses...

doc/topic-networks.tex

@@ -55,7 +55,8 @@
 
 \title[Topic Networks]{
        Topic Networks \\
-       {\Large A mini project for Social Network Analysis}
+       {\Large A mini project for Social Network Analysis} \\
+       {\large Final Version}
 }
 %\author[Bob Flagg]{Bob Flagg}
 
@@ -300,7 +301,8 @@ \subsection{The Topic Network}
 
 \begin{verbatim}
 # Create the topic network:
-topic.network.matrix <- t(dt.matrix) %*% dt.matrix
+topic.network.matrix <- t(dt.matrix) %*% 
+  dt.matrix
 topic.network <- graph.adjacency(
   topic.network.matrix, mode = "undirected")
 \end{verbatim}
@@ -337,6 +339,39 @@ \subsection{The Topic Network}
 \label{fig:topic-network}
 \end{figure}
 
+As Figure~\ref{fig:topic-network} shows, the topic network is very busy, suggesting
+that we've not done a good job choosing the most import topics for each document.
+In fact, as the code below shows, the average degree, at $19.3$, is very high.
+
+\begin{verbatim}
+# Compute the average degree of our network:
+degrees <- V(topic.network)$degree
+topic.network.average.degree <- sum(degrees) / 
+  length(V(topic.network))
+\end{verbatim}
+
+\noindent This problem can probably be fixed if rather than taking the top 4 topics for each
+document in the document-topic network, we were to choose only those topics whose
+probability of appearing in the document is above a certain threshold.  We plan to 
+investigate that approach but don't have time to pursue it here.
+
+Once we've solved the previous problem, we plan to systematically investigate the connections between important
+properties of the topic network and the underlying corpus.  As an example, consider
+centrality:
+
+\begin{verbatim}
+# Betweenness centrality
+V(topic.network)$btwcnt <- betweenness(topic.network)
+V(topic.network)$label[order(V(topic.network)$btwcnt)]
+\end{verbatim}
+
+\noindent This measure suggests that the most central topics in the corpus are
+\begin{itemize}
+ \item tonight, mccain, page
+ \item religion, bankruptcy, christian
+ \item oil, fuel, auto
+ \item iraq, iraqi, troop
+\end{itemize}
 
 
 \subsection{The Overlap Network}

r/topic-networks.R

@@ -25,6 +25,7 @@
 # Set the path to the corpus directory.                                        #
 # ---------------------------------------------------------------------------- #
 corpus.directory <- '/home/birksworks/Projects/topic-networks/corpus'
+setwd('/home/birksworks/Projects/topic-networks/Topic-Networks/doc/')
 # ---------------------------------------------------------------------------- #
 # Load required libraries.                                                     #
 # ---------------------------------------------------------------------------- #
@@ -125,8 +126,12 @@ V(dt.network)$size[1:n.docs] <- 2
 V(dt.network)$size[(n.docs+1):n.vertices] <- 6
 E(dt.network)$width <- .5
 E(dt.network)$color <- rgb(.5,.5,0,.4)
+tkplot(dt.network)
+dt.network$layout <- tkplot.getcoords(1)
+
 pdf("dtn.pdf")
 plot(dt.network, layout=layout.fruchterman.reingold)
+plot(dt.network)
 dev.off()
 png("dtn.png")
 plot(dt.network, layout=layout.fruchterman.reingold)
@@ -149,6 +154,9 @@ V(topic.network)$color <- rgb(0,1,0,.6)
 # Set edge gamma according to edge weight
 egam <- (log(E(topic.network)$weight)+.3)/max(log(E(topic.network)$weight)+.3)
 E(topic.network)$color <- rgb(.5,.5,0,egam)
+tkplot(topic.network)
+topic.network$layout <- tkplot.getcoords(2)
+
 pdf("topic-network.pdf")
 plot(topic.network, layout=layout.kamada.kawai)
 dev.off()
@@ -175,7 +183,7 @@ overlap.network <- simplify(overlap.network, remove.multiple=FALSE, remove.loops
 overlap.network$layout <- layout.kamada.kawai(overlap.network)
 V(overlap.network)$label <- topic.labels
 tkplot(overlap.network)
-overlap.network$layout <- tkplot.getcoords(1)
+overlap.network$layout <- tkplot.getcoords(3)
 
 # Set vertex attributes
 V(overlap.network)$label.color <- rgb(0,0,.2,.6)