gostyle.tex: nn, training

[gostyle.git] / tex / gostyle.tex

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\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
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\title{On Pattern Feature Trends in Large Go Game Corpus}

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\thanks{P. Baudis is student at the Faculty of Math and Physics, Charles University, Prague, CZ, and also does some of his Computer Go research as an employee of SUSE Labs Prague, Novell CZ.}% <-this % stops a space
\thanks{J. Moudrik is student at the Faculty of Math and Physics, Charles University, Prague, CZ.}}

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\markboth{Transactions on Computational Intelligence and AI in Games}%
{On Pattern Feature Trends in Large Go Game Corpus}
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\begin{abstract}
%\boldmath

We process a~large corpus of game records of the board game of Go and
propose a~way to extract per-player summary information on played moves.
We then apply several basic data-mining methods on the summary
information to identify the most differentiating features within the
summary information, and discuss their correspondence with traditional
Go knowledge. We show mappings of the features to player attributes
like playing strength or informally perceived "playing style" (such as
territoriality or aggressivity), and propose applications including
seeding real-work ranks of internet players, aiding in Go study, or
contribution to discussion within Go theory on the scope of "playing
style".

\end{abstract}
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\begin{IEEEkeywords}
board games, go, data mining, player strength, playing style
\end{IEEEkeywords}






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\section{Introduction}
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\IEEEPARstart{T}{he} field of Computer Go usually focuses on the problem
of creating a~program to play the game, finding the best move from a~given
board position. We will make use of one method developed in the course
of such research and apply it to the analysis of existing game records
with the aim of helping humans to play the game better instead.

Go is a~two-player full-information board game played
on a~square grid (usually $19\times19$ lines) with black and white
stones; the goal of the game is to surround the most territory and
capture enemy stones. We assume basic familiarity with the game.

Many Go players are eager to play using computers (usually over
the internet) and review games played by others on computers as well.
This means that large amounts of game records are collected and digitally
stored, enabling easy processing of such collections. However, so far
only little has been done with the available data --- we are aware
only of uses for simple win/loss statistics (TODO: KGS Stats, KGS Analytics,
Pro Go Rating) and ''next move'' statistics on a~specific position (TODO:
Kombilo, Moyo Go Studio).

We present a~more in-depth approach --- from all played moves, we devise
a~compact evaluation of each player. We then explore correlations between
evaluations of various players in light of externally given information.
This way, we can discover similarity between moves characteristics of
players with the same playing strength, or discuss the meaning of the
"playing style" concept on the assumption that similar playing styles
should yield similar moves characteristics.


\section{Expert-based knowledge}
\label{style-vectors}
In order to provide a reference frame for our style analysis,
we have gathered some expert-based information about various
traditionally perceived style aspects.
Three high-level Go players (Alexander Dinerstein 3-pro, Motoki Noguchi
7-dan and Vit Brunner 4-dan) have judged style of several Go
professionals (chosen for both being well-known within the community
and having large number of played games in our collection).

This expert-based knowledge allows us to predict styles of unknown players based on
the similarity of their pattern vectors, as well as discover correlations between
styles and proportions of played patterns.

Experts were asked to assign each of player's style a number
on a scale from 1 to 10. These are interpreted
as shown in the table below.

\vspace{4mm}
\noindent
%\begin{table}
\begin{center}
%\caption{Styles}
\begin{tabular}{|c|c|c|}
\hline
\multicolumn{3}{|c|}{Styles} \\ \hline
Style & 1 & 10\\ \hline
Territoriality & Moyo & Territorial \\
Orthodoxity & Classic & Novel \\
Aggressivity & Calm & Figting \\
Thickness & Safe & Shinogi \\ \hline
\end{tabular}
\end{center}
%\end{table}

Averaging and rescaling the expert based evaluation yields a set of
\emph{reference style vectors} $\vec s_r$. 
%-- each with a \emph{pattern vector} $\vec p_i$ and \emph{style vector} $\vec s_i$.


\section{Data Extraction}
\label{pattern-vectors}

As the input of our method, we assume a~collection of game records\footnote{We
use the SGF format (TODO) in our implementation.} organized by player names.
We use two collections; the first one is GoGoD Winter 2009 (TODO) containing 42000 (TODO)
professional games, dating from the early Go history 1500 years ago to the present.
We use this collection for style analysis and detailed correlation analysis
of well-known Go professionals.
The other source is Go Teaching Ladder reviews (TODO). These include 7600 games
of players spanning over all strength levels; we use this collection
for finding correlations between moves of players of the same strength rank.

In order to generate the required compact description of most played moves,
for each player, we extract a~generic description from each move
played by the player, then take the most occuring $n$ patterns across all players%
\footnote{We use $n=500$ in our analysis.} and assign each player a~{\em pattern vector}
$\vec p$ where each dimension corresponds to the number of occurences of
one given pattern normalized to range $[0,1]$.

\subsection{Pattern Features}

Of course a big question is how to compose the pattern descriptions.
There are some tradeoffs in play - overly general descriptions carry too few
information to discern various player attributes; too specific descriptions
gather too few specimen over the games and the differences in vectors are
not statistically significant.

We have chosen an intuitive and simple approach inspired by pattern features
used when computing ELO ratings for candidate patterns in Computer Go play.
\cite{ELO} Each pattern is combination of several {\em pattern features}
matched at the position of the played move. We use these features:

\begin{itemize}
\item board edge distance
\item capture move flag
\item atari move flag
\item atari escape flag
\item spatial pattern --- a configuration of stones around the played move,
with differentiated color to play; configurations with diameter between
2 and 9 are matched\footnote{The diameter determines maximal distance from
center in the {\em gridcular} metric: $d(x,y) = |\delta x| + |\delta y| + \max(|\delta x|, |\delta y|)$}
\end{itemize}

\subsection{Implementation}

We have implemented the data extraction by making use of the pattern
features matching implementation within the Pachi go-playing program
(TODO). We extract information on players by converting the SGF game
records to GTP (TODO) stream that feeds Pachi's {\tt patternscan}
engine which outputs a~single patternspec per move. We can then gather
all encountered patternspecs belonging to a~given player and summarize
them; the $\vec p$ vector then consists of normalized counts of
the given $n$ most frequent patternspecs.


\section{Data Mining}
\label{data-mining}
To assess the properties of gathered \emph{pattern vectors} and their influence on playing styles,
we have analysed the data by a~few basic data minining techniques.

TODO PCA: We use it either on it own, or as a~pre-processing making data suitable for other methods.

TODO rozdelit na algo/results?? 

\subsection{Principal Component Analysis}
\label{data-mining}
Principal Component Analysis \emph{PCA} \cite{Jolliffe1986} is a~method we use to reduce the dimensions of
\emph{pattern vectors} while preserving as much information as possible.

Shortly, PCA is an eigenvalue decomposition of a~covariance matrix of centered \emph{pattern vectors}.
It can be thought of as a~mapping $o$ from $n$-dimensional vector space to a~reduced $m$-dimensional vector space.
The base of this reduced vector space comprises $m$ eigenvectors of original vectors' covariance matrix.
We choose them to be the eigenvectors with biggest eigenvalues. 
Ordered by decreasing eigenvalues, the eigenvectors form rows of the transformation matrix $W$.

Finally, we represent reduced \emph{pattern vectors} as a vector of coeficients of this eigenvector-base.
For each original \emph{pattern vector} $\vec p_i$, we obtain its new representation $\vec r_i$ as shown
in the following equation:
\begin{equation}
\vec r_i = W * \vec p_i
\end{equation}

The whole process is described in the Algorithm \ref{alg:pca}.

\begin{algorithm}
\caption{PCA -- Principal Component analysis}
\begin{algorithmic}[1]
\label{alg:pca}
\REQUIRE{$m > 0$, set of players $R$ with \emph{pattern vectors} $p_r$}
\STATE $\vec \mu \leftarrow 1/|R| * \sum_{r \in R}{\vec p_r}$
\FOR{ $r \in R$}
\STATE $\vec p_r \leftarrow \vec p_r - \vec \mu$
\ENDFOR
\FOR{ $(i,j) \in \{1,... ,n\} \times \{1,... ,n\}$}
\STATE $Cov[i,j] \leftarrow 1/|R| * \sum_{r \in R}{\vec p_{ri} * \vec p_{rj}}$
\ENDFOR
\STATE Compute Eigenvalue Decomposition of $Cov$ matrix
\STATE Get $m$ biggest eigenvalues 
\STATE According eigenvectors ordered by decreasing eigenvalues form rows of matrix $W$ 
\FOR{ $r \in R$}
\STATE $\vec r_r\leftarrow W \vec p_r$
\ENDFOR
\end{algorithmic}
\end{algorithm}

\subsection{Kohonen Maps}

\subsection{k-nearest Neighbors Classifier}
\label{knn}
K-nearest neigbors is an essential classification technique.
We use it to approximate player's \emph{style vector} $\vec S$, assuming that his \emph{pattern vector} $\vec P$ is known.
To achieve this, we utilize \emph{reference style vectors} (see section \ref{style-vectors}).

The idea is based on a assumption that similarities in players' \emph{pattern vectors}
correlate with similarities in players' \emph{style vectors}. We try to approximate $\vec S$
as a weighted average of \emph{style vectors}
$\vec s_i$ of $k$ players with \emph{pattern vectors} $\vec p_i$ closest to $\vec P$.
This is illustrated in the Algorithm \ref{alg:knn}.
Note that the weight is a function of distance and it is not explicitly defined in Algorithm \ref{alg:knn}.
During our research, exponentialy decreasing weight has proven to be sufficient.

\begin{algorithm}
\caption{k-Nearest Neighbors}
\begin{algorithmic}
\label{alg:knn}
\REQUIRE{pattern vector $\vec P$, $k > 0$, set of reference players $R$}
\FORALL{r $\in$ R }
\STATE $D[r] \leftarrow EuclideanDistance(\vec p_r, \vec P)$
\ENDFOR
\STATE $N \leftarrow SelectSmallest(k, R, D)$
\STATE $\vec S \leftarrow \vec 0$
\FORALL{r $\in$ N }
\STATE $\vec S \leftarrow \vec S + Weight(D[r]) * \vec s_r $
\ENDFOR
\end{algorithmic}
\end{algorithm}

\subsection{Neural Network Classifier}
\label{neural-net}

As an alternative to the k-Nearest Neigbors algorithm (section \ref{knn}), we have used 
a classificator based on feed-forward artificial neural networks \cite{TODO}.
Neural networks (NN) are known for their ability to generalize and find correlations and patterns between
input and output data. Neural network is an adaptive system and it 
must undergo a certain training before it can be reasonably used. Basically, we use
information for \emph{reference players} (for which either \emph{pattern vectors} and
\emph{style vectors} are known) as training data.

\subsubsection{Computation and activation of the NN}
Technically, neural network is a network of interconnected computational units called neurons.
A feedforward neural network has a layered topology; it usually has one \emph{input layer}, one \emph{output
layer} and an arbitrary number of \emph{hidden layers} between.

Each neuron $i$ is connected to all neurons in the previous layer and each connection has its weight $w_{ij}$

The computation proceeds in a discrete time steps.
In the first step, \emph{activation} of neurons in the \emph{input layer} is set according to the \emph{input vector}.
Then, we iteratively compute output of each neuron in next layer until the output layer is reached. The activity of
output layer is then presented as a result.

The activation $y_i$ of neuron $i$ from the layer $I$ is computed using the following equation:
\begin{equation}
y_i = f(\sum_{j \in J}{w_{ij} y_j})
\end{equation}
where $J$ is a previous layer, while $y_j$ is the activation for neurons from $J$ layer. Function $f()$ is
called \emph{activation function} and its purpose is to bound outputs of neurons. A typical example of an activation
function is a sigmoid function.\footnote{The sigmoid function is a special case of the logistic function; it is defined by the formula
$\sigma(x)=\frac{1}{1+e^{-(rx+k)}}$, parameters control the growth rate ($r$) and the x-position ($k$).}

\subsubsection{Training}
The training of the feedforward neural network usually involves some
modification of supervised Backpropagation learning algorithm. \cite{TODO}
We use first-order optimization algorithm called RPROP \cite{TODO}.

Because the \emph{reference set} is not usually very large, we have devised a simple method for its extension.
This enhancement is based upon adding random linear combinations of \emph{style and pattern vectors} to the training set.

As insinuated above, the training set consist of pairs of input vectors (\emph{pattern vectors}) and
desired output vectors (\emph{style vectors}). The training set $T$ is then enlarged by some linear combinations.
\begin{equation}
T_{base} = \{(\vec p_r, \vec s_r) | r \in R\}\\
\end{equation}
\begin{equation}
T_{ext} = \{(\vec p, \vec s) | \exists D \supseteq R : p = \sum_{d \in D}{g_d \vec p_d}, s = \sum_{d \in D}{g_d \vec s_d}\}
\end{equation}
TODO zabudovat $g_d$ dovnitr?
where $g_d, d \in D$ are random coeficients, so that $\sum_{d \in D}{g_d} = 1$. The training set
is then obtained by:
\begin{equation}
T = T_{base} \cup SomeFiniteSubset(T_{ext})
\end{equation}

The network is trained by repeat

\subsubsection{Architecture details}



\subsection{Implementation}


We have implemented the data mining methods as an open-source project
``gostyle'' (TODO). TODO.
PCA: In our implementation, we use a~library called MDP \cite{MDP}.
TODO libfann


\section{Style Components Analysis}


\section{Strength Estimation Analysis}


\section{Proposed Applications}


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% and a .pdf suffix will be assumed for pdflatex; or what has been declared
% via \DeclareGraphicsExtensions.
%\caption{Simulation Results}
%\label{fig_sim}
%\end{figure}

% Note that IEEE typically puts floats only at the top, even when this
% results in a large percentage of a column being occupied by floats.


% An example of a double column floating figure using two subfigures.
% (The subfig.sty package must be loaded for this to work.)
% The subfigure \label commands are set within each subfloat command, the
% \label for the overall figure must come after \caption.
% \hfil must be used as a separator to get equal spacing.
% The subfigure.sty package works much the same way, except \subfigure is
% used instead of \subfloat.
%
%\begin{figure*}[!t]
%\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
%\label{fig_first_case}}
%\hfil
%\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
%\label{fig_second_case}}}
%\caption{Simulation results}
%\label{fig_sim}
%\end{figure*}
%
% Note that often IEEE papers with subfigures do not employ subfigure
% captions (using the optional argument to \subfloat), but instead will
% reference/describe all of them (a), (b), etc., within the main caption.


% An example of a floating table. Note that, for IEEE style tables, the 
% \caption command should come BEFORE the table. Table text will default to
% \footnotesize as IEEE normally uses this smaller font for tables.
% The \label must come after \caption as always.
%
%\begin{table}[!t]
%% increase table row spacing, adjust to taste
%\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of
% \extrarowheight as needed to properly center the text within the cells
%\caption{An Example of a Table}
%\label{table_example}
%\centering
%% Some packages, such as MDW tools, offer better commands for making tables
%% than the plain LaTeX2e tabular which is used here.
%\begin{tabular}{|c||c|}
%\hline
%One & Two\\
%\hline
%Three & Four\\
%\hline
%\end{tabular}
%\end{table}


% Note that IEEE does not put floats in the very first column - or typically
% anywhere on the first page for that matter. Also, in-text middle ("here")
% positioning is not used. Most IEEE journals use top floats exclusively.
% Note that, LaTeX2e, unlike IEEE journals, places footnotes above bottom
% floats. This can be corrected via the \fnbelowfloat command of the
% stfloats package.



\section{Conclusion}
The conclusion goes here.
We have shown brm and proposed brm.

Since we are not aware of any previous research on this topic and we
are limited by space and time constraints, plenty of research remains
to be done. There is plenty of room for further research in all parts
of our analysis --- different methods of generating the $\vec p$ vectors
can be explored; other data mining methods could be tried.
It can be argued that many players adjust their style by game conditions
(Go development era, handicap, komi and color, time limits, opponent)
or styles might express differently in various game stages.
Finally, more professional players could be consulted on the findings
and for style scales calibration.

TODO: Future research --- Sparse PCA




% if have a single appendix:
%\appendix[Proof of the Zonklar Equations]
% or
%\appendix  % for no appendix heading
% do not use \section anymore after \appendix, only \section*
% is possibly needed

% use appendices with more than one appendix
% then use \section to start each appendix
% you must declare a \section before using any
% \subsection or using \label (\appendices by itself
% starts a section numbered zero.)
%


%\appendices
%\section{Proof of the First Zonklar Equation}
%Appendix one text goes here.
%
%% you can choose not to have a title for an appendix
%% if you want by leaving the argument blank
%\section{}
%Appendix two text goes here.


% use section* for acknowledgement
\section*{Acknowledgment}
\label{acknowledgement}


We would like to thank X for reviewing our paper.
We appreciate helpful comments on our general methodology
by John Fairbairn, T. M. Hall, Robert Jasiek
and several GoDiscussions.com users. \cite{GoDiscThread}
Finally, we are very grateful for ranking of go styles of selected professionals
by Alexander Dinerstein 3-pro, Motoki Noguchi 7-dan and Vit Brunner 4-dan.


% Can use something like this to put references on a page
% by themselves when using endfloat and the captionsoff option.
\ifCLASSOPTIONcaptionsoff
  \newpage
\fi



% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
\bibliography{gostyle}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
%\begin{thebibliography}{1}
%
%\bibitem{MasterMCTS}
%
%\end{thebibliography}

% biography section
% 
% If you have an EPS/PDF photo (graphicx package needed) extra braces are
% needed around the contents of the optional argument to biography to prevent
% the LaTeX parser from getting confused when it sees the complicated
% \includegraphics command within an optional argument. (You could create
% your own custom macro containing the \includegraphics command to make things
% simpler here.)
%\begin{biography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
% or if you just want to reserve a space for a photo:

\begin{IEEEbiography}{Michael Shell}
Biography text here.
\end{IEEEbiography}

% if you will not have a photo at all:
\begin{IEEEbiographynophoto}{John Doe}
Biography text here.
\end{IEEEbiographynophoto}

% insert where needed to balance the two columns on the last page with
% biographies
%\newpage

\begin{IEEEbiographynophoto}{Jane Doe}
Biography text here.
\end{IEEEbiographynophoto}

% You can push biographies down or up by placing
% a \vfill before or after them. The appropriate
% use of \vfill depends on what kind of text is
% on the last page and whether or not the columns
% are being equalized.

%\vfill

% Can be used to pull up biographies so that the bottom of the last one
% is flush with the other column.
%\enlargethispage{-5in}



% that's all folks
\end{document}