From b0de41c5754dba217efcf235f697a354e07b4e5c Mon Sep 17 00:00:00 2001 From: Petr Baudis Date: Sat, 13 Mar 2010 23:48:31 +0100 Subject: [PATCH] tex: -Kohonen map, +Sociomap (TODO: algo. descr.) --- tex/gostyle.bib | 14 + tex/gostyle.tex | 92 +- tex/makefile | 2 +- tex/sociomap.eps | 55514 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 4 files changed, 55561 insertions(+), 61 deletions(-) create mode 100644 tex/sociomap.eps diff --git a/tex/gostyle.bib b/tex/gostyle.bib index 21a0a82..11ea184 100644 --- a/tex/gostyle.bib +++ b/tex/gostyle.bib @@ -93,6 +93,20 @@ url = {http://repo.or.cz/w/gostyle.git} } +@ELECTRONIC{TPA, + author = {{\relax QED} GROUP}, + title = {Team Profile Analyzer}, + owner = {pasky}, + url = {http://www.teamprofileanalyzer.com/} +} + +@ELECTRONIC{SociomapSite, + author = {{\relax QED} GROUP}, + title = {Sociomapping Suite}, + owner = {pasky}, + url = {http://www.sociomap.com/} +} + @inproceedings{SpatPat, author = {Stern, David and Herbrich, Ralf and Graepel, Thore}, title = {Bayesian pattern ranking for move prediction in the game of Go}, diff --git a/tex/gostyle.tex b/tex/gostyle.tex index 1d08ac3..6f36a02 100644 --- a/tex/gostyle.tex +++ b/tex/gostyle.tex @@ -300,7 +300,7 @@ style''. \begin{IEEEkeywords} board games, go, computer go, data mining, go theory, pattern recongition, player strength, playing style, -neural networks, Kohonen maps, principal component analysis, +neural networks, sociomaps, principal component analysis, naive bayes classifier \end{IEEEkeywords} @@ -503,12 +503,8 @@ Reversing the process can indicate which patterns correlate with each component. Additionally, PCA can be used as vector preprocessing for methods that are negatively sensitive to pattern vector component correlations. -The~second method of Kohonen Maps -is based on the theory of self-organizing maps of abstract units (neurons) that -compete against each other for the representation of the input space. -Because neurons in the network are organized in a two-dimensional plane, -the trained network spreads the vectors on a 2D plane, -allowing for visualization of clusters of players with similar properties. +The~second method of Sociomaps +is TODO TODO TODO. Furthermore, we test several \emph{classification} methods that assign @@ -597,54 +593,9 @@ between the dimensions: $$ r_{X,Y} = {{\rm cov}(X,Y) \over \sigma_X \sigma_Y} $$ -\subsection{Kohonen Maps} -\label{koh} -Kohonen map is a self-organizing network with neurons spread evenly over a~two-dimensional plane. -Neurons $\vec n$ in the map compete for representation of portions of the input vector space, -each vector being represented by some neuron. -The network is trained so that the neurons -that are topologically close tend to represent vectors that are close in suitable metric as well. - -First, a~randomly initialized network is sequentially trained; -in each iteration, we choose a~random training vector $\vec t$ -and find the {\em winner neuron} $\vec w$ that is closest to $\vec t$ in Euclidean metric. - -We then adapt neurons $n$ from the neighborhood of $\vec w$ employing the equation -\begin{equation} -\vec n = \vec n + \alpha \cdot \mathit{Influence}(\vec w, \vec n) \cdot (\vec t - \vec n) -\end{equation} -where $\alpha$ is a learning parameter, usually decreasing in time. -$Influence()$ is a function that forces neurons to spread. -Such function is usually realised using a mexican hat function or a difference-of-gaussians -\cite{TODO}. -The state of the network can be evaluated by calculating mean square difference -between each $\vec t \in T$ and its corresponding winner neuron $\vec w_t$: -\begin{equation} -\mathit{Error}(N,T) = \sum_{\vec t \in T}{|\vec w_t - \vec t|} -\end{equation} - - -\begin{algorithm} -\caption{Kohonen maps -- training} -\begin{algorithmic} -\label{alg:koh} -\REQUIRE{Set of training vectors $T$, input dimension $D$} -\REQUIRE{max number of iterations $M$, desired error $E$} -\STATE $N \leftarrow \{\vec n | \vec n$ random, $\mathit{dim}(\vec n) = D\}$ -\REPEAT -\STATE $\mathit{It} \leftarrow \mathit{It} + 1$ -\STATE $\vec t \leftarrow \mathit{PickRandom}(T)$ -\FORALL{$\vec n \in N$} -\STATE $D[\vec n] \leftarrow \mathit{EuclideanDistance}(\vec n, \vec t)$ -\ENDFOR -\STATE Find $ \vec w \in N$ so that $D[\vec w] <= D[\vec m], \forall \vec m \in N$ -\FORALL{$\vec n \in \mathit{TopologicalNeigbors}(N, \vec w)$} -\STATE $\vec n \leftarrow \vec n + \alpha(It) \cdot \mathit{Influence}(\vec w, \vec n) \cdot ( \vec t - \vec n ) $ -\ENDFOR -\UNTIL{$\mathit{Error}(N, T) < E$ or $ \mathit{It} > M$} -\end{algorithmic} -\end{algorithm} - +\subsection{Sociomaps} +\label{soc} +TODO TODO. \subsection{k-nearest Neighbors Classifier} \label{knn} @@ -819,10 +770,12 @@ made available under the GNU GPL licence. The majority of our basic processing and the analysis parts are implemented in the Python \cite{Python25} programming language. -We use several external libraries, most notably the MDP library \cite{MDP} (used for PCA analysis) -and Kohonen library \cite{KohonenPy}. +We use several external libraries, most notably the MDP library \cite{MDP}. The neural network part of the project is written using the libfann C library\cite{Nissen2003}. +The sociomap has been visualised using the Team Profile Analyzer \cite{TPA} +which is part of the Sociomap suite \cite{SociomapSite}. + \section{Strength Estimator} @@ -1296,11 +1249,30 @@ However, we do not use the extended normalization results since they produced noticeably less accurate classifiers in all dimensions, including $\omega$ and $\alpha$. +\begin{figure}[!t] +\centering +\includegraphics[width=3.5in,angle=-90]{sociomap} +\caption{Sociomap visualisation. The spatial positioning of players +is based on the expert knowledge, while the node heights (depicted by +contour lines) represent the pattern vectors.% +%The light lines denote coherence-based hierarchical clusters. +} +\label{fig:sociomap} +\end{figure} + +Fig. \ref{fig:sociomap} shows the Sociomap visualisation +as an alternate view of the player relationships and similarity, +as well as correlation between the expert-given style marks +and the PCA decomposition. The four-dimensional style vectors +are used as input for the Sociomap renderer and determine the +spatial positions of players. The height of a node is then +determined using first two PCA dimensions $R_1,R_2$ and their +eigenvalues $\lambda_1,\lambda_2$ as their linear combination: +$$ h=\lambda_1R_1 + \lambda_2R_2 $$ + We believe that the next step in interpreting our results will be more refined prior information input -and precise analysis by Go experts. - -TODO: Kohonen map view. 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