tex: Elaborate somewhat on the extracted patterns
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203 \hyphenation{op-tical net-works semi-conduc-tor}
206 \begin{document}
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210 \title{On Pattern Feature Trends in Large Go Game Corpus}
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215 \author{Petr~Baudis,~Josef~Moudrik% <-this % stops a space
216 \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
217 \thanks{J. Moudrik is student at the Faculty of Math and Physics, Charles University, Prague, CZ.}}
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239 \markboth{Transactions on Computational Intelligence and AI in Games}%
240 {On Pattern Feature Trends in Large Go Game Corpus}
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270 \begin{abstract}
271 %\boldmath
273 We process a~large corpus of game records of the board game of Go and
274 propose a~way to extract per-player summary information on played moves.
275 We then apply several basic data-mining methods on the summary
276 information to identify the most differentiating features within the
277 summary information, and discuss their correspondence with traditional
278 Go knowledge. We show mappings of the features to player attributes
279 like playing strength or informally perceived "playing style" (such as
280 territoriality or aggressivity), and propose applications including
281 seeding real-work ranks of internet players, aiding in Go study, or
282 contribution to discussion within Go theory on the scope of "playing
283 style".
285 \end{abstract}
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294 \begin{IEEEkeywords}
295 board games, go, data mining, player strength, playing style
296 \end{IEEEkeywords}
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315 \section{Introduction}
316 % The very first letter is a 2 line initial drop letter followed
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330 % and "HIS" in caps to complete the first word.
331 \IEEEPARstart{T}{he} field of Computer Go usually focuses on the problem
332 of creating a~program to play the game, finding the best move from a~given
333 board position. We will make use of one method developed in the course
334 of such research and apply it to the analysis of existing game records
335 with the aim of helping humans to play the game better instead.
337 Go is a~two-player full-information board game played
338 on a~square grid (usually $19\times19$ lines) with black and white
339 stones; the goal of the game is to surround the most territory and
340 capture enemy stones. We assume basic familiarity with the game.
342 Many Go players are eager to play using computers (usually over
343 the internet) and review games played by others on computers as well.
344 This means that large amounts of game records are collected and digitally
345 stored, enabling easy processing of such collections. However, so far
346 only little has been done with the available data --- we are aware
347 only of uses for simple win/loss statistics (TODO: KGS Stats, KGS Analytics,
348 Pro Go Rating) and ''next move'' statistics on a~specific position (TODO:
349 Kombilo, Moyo Go Studio).
351 We present a~more in-depth approach --- from all played moves, we devise
352 a~compact evaluation of each player. We then explore correlations between
353 evaluations of various players in light of externally given information.
354 This way, we can discover similarity between moves characteristics of
355 players with the same playing strength, or discuss the meaning of the
356 "playing style" concept on the assumption that similar playing styles
357 should yield similar moves characteristics.
360 \section{Data Extraction}
361 TODO gen intro into data extr
363 \subsection{Pattern feature based extraction} TODO redo this XXX caption
364 \label{pattern-vectors}
366 As the input of our method, we assume a~collection of game records\footnote{We
367 use the SGF format (TODO) in our implementation.} organized by player names.
368 We use two collections; the first one is GoGoD Winter 2009 (TODO) containing 42000 (TODO)
369 professional games, dating from the early Go history 1500 years ago to the present.
370 We use this collection for style analysis and detailed correlation analysis
371 of well-known Go professionals.
372 The other source is Go Teaching Ladder reviews (TODO). These include 7600 games
373 of players spanning over all strength levels; we use this collection
374 for finding correlations between moves of players of the same strength rank.
376 In order to generate the required compact description of most played moves,
377 for each player, we extract a~generic description from each move
378 played by the player, then take the most occuring $n$ patterns across all players%
379 \footnote{We use $n=500$ in our analysis.} and assign each player a~{\em pattern vector}
380 $\vec d$ where each dimension corresponds to the number of occurences of
381 one given pattern normalized to range $[0,1]$.
383 \subsection{Pattern Features}
385 Of course a big question is how to compose the pattern descriptions.
386 There are some tradeoffs in play - overly general descriptions carry too few
387 information to discern various player attributes; too specific descriptions
388 gather too few specimen over the games and the differences in vectors are
389 not statistically significant.
391 We have chosen an intuitive and simple approach inspired by pattern features
392 used when computing ELO ratings for candidate patterns in Computer Go play.
393 \cite{ELO} Each pattern is combination of several {\em pattern features}
394 matched at the position of the played move. We use these features:
396 \begin{itemize}
397 \item TODO
398 \end{itemize}
400 \subsection{Expert-based knowledge}
401 \label{style-vectors}
402 Apart from the pattern vectors extracted from game collections, we have gathered some
403 expert-based information about (simplified) traditional-meaning playing styles.
404 We have asked several high-level Go players (see the acknowledgement \ref{acknowledgement})
405 to explicitly evaluate styles for some well-known Go players.
406 \footnote{The well-known Go players were incidentally chosen so that a rich
407 set of their games is present in the GoGoD 2009 collection.}
409 This expert-based knowledge allows us to predict styles of unknown players based on
410 the similarity of their pattern vectors, as well as discover correlations between
411 styles and proportions of played patterns.
413 Experts were asked to assign each of player's style (including territoriality, orthodoxity,
414 aggressivity, thickness) a number on a scale from 1 to 10. These are interpreted
415 as shown in the table below.
417 \vspace{4mm}
418 \noindent
419 %\begin{table}
420 \begin{center}
421 %\caption{Styles}
422 \begin{tabular}{|c|c|c|}
423 \hline
424 \multicolumn{3}{|c|}{Styles} \\ \hline
425 Style & 1 & 10\\ \hline
426 Territoriality & Moyo & Territorial \\
427 Orthodoxity & Classic & Novel \\
428 Aggressivity & Calm & Figting \\
429 Thickness & Safe & Shinogi \\ \hline
430 \end{tabular}
431 \end{center}
432 %\end{table}
434 Averaging and rescaling the expert based evaluation yields a set of
435 \emph{reference style vectors} $\vec s_r$.
436 %-- each with a \emph{pattern vector} $\vec p_i$ and \emph{style vector} $\vec s_i$.
438 \subsection{Implementation}
440 We have implemented the data extraction by making use of the pattern
441 features matching implementation within the Pachi go-playing program
442 (TODO). We extract information on players by converting the SGF game
443 records to GTP (TODO) stream that feeds Pachi's {\tt patternscan}
444 engine which outputs a~single patternspec per move. We can then gather
445 all encountered patternspecs belonging to a~given player and summarize
446 them; the $\vec p$ vector then consists of normalized counts of
447 the given $n$ most frequent patternspecs.
450 \section{Data Mining}
451 To assess the properties of gathered \emph{pattern vectors} and their influence on playing styles,
452 we have analysed the data by a~few basic data minining techniques.
454 TODO PCA: We use it either on it own, or as a~pre-processing making data suitable for other methods.
456 TODO rozdelit na algo/results??
458 \subsection{Principal Component Analysis}
459 Principal Component Analysis \emph{PCA} \cite{Jolliffe1986} is a~method we use to reduce the dimensions of
460 \emph{pattern vectors} while preserving as much information as possible.
462 Shortly, PCA is an eigenvalue decomposition of a~covariance matrix of centered \emph{pattern vectors}.
463 It can be thought of as a~mapping $o$ from $n$-dimensional vector space to a~reduced $m$-dimensional vector space.
464 The base of this reduced vector space comprises $m$ eigenvectors of original vectors' covariance matrix.
465 We choose them to be the eigenvectors with biggest eigenvalues.
466 Ordered by decreasing eigenvalues, the eigenvectors form rows of the transformation matrix $W$.
468 Finally, we represent reduced \emph{pattern vectors} as a vector of coeficients of this eigenvector-base.
469 For each original \emph{pattern vector} $\vec p_i$, we obtain its new representation $\vec r_i$ as shown
470 in the following equation:
471 \begin{equation}
472 \vec r_i = W * \vec p_i
473 \end{equation}
475 The whole process is described in the Algorithm \ref{alg:pca}.
477 \begin{algorithm}
478 \caption{PCA -- Principal Component analysis}
479 \begin{algorithmic}[1]
480 \label{alg:pca}
481 \REQUIRE{$m > 0$, set of players $R$ with \emph{pattern vectors} $p_r$}
482 \STATE $\vec \mu \leftarrow 1/|R| * \sum_{r \in R}{\vec p_r}$
483 \FOR{ $r \in R$}
484 \STATE $\vec p_r \leftarrow \vec p_r - \vec \mu$
485 \ENDFOR
486 \FOR{ $(i,j) \in \{1,... ,n\} \times \{1,... ,n\}$}
487 \STATE $Cov[i,j] \leftarrow 1/|R| * \sum_{r \in R}{\vec p_{ri} * \vec p_{rj}}$
488 \ENDFOR
489 \STATE Compute Eigenvalue Decomposition of $Cov$ matrix
490 \STATE Get $m$ biggest eigenvalues
491 \STATE According eigenvectors ordered by decreasing eigenvalues form rows of matrix $W$
492 \FOR{ $r \in R$}
493 \STATE $\vec r_r\leftarrow W \vec p_r$
494 \ENDFOR
495 \end{algorithmic}
496 \end{algorithm}
498 \subsection{?? Kohonen Maps ??}
500 \subsection{k-nearest Neighbors Classifier}
501 K-nearest neigbors is an essential classification technique.
502 We use it to approximate player's \emph{style vector} $\vec S$, assuming that his \emph{pattern vector} $\vec P$ is known.
503 To achieve this, we utilize \emph{reference style vectors} (see section \ref{style-vectors}).
505 The idea is based on a assumption that similarities in players' \emph{pattern vectors}
506 correlate with similarities in players' \emph{style vectors}. We try to approximate $\vec S$
507 as a weighted average of \emph{style vectors}
508 $\vec s_i$ of $k$ players with \emph{pattern vectors} $\vec p_i$ closest to $\vec P$.
509 This is illustrated in the Algorithm \ref{alg:knn}.
510 Note that the weight is a function of distance and it is not explicitly defined in Algorithm \ref{alg:knn}.
511 During our research, exponentialy decreasing weight has proven to be sufficient.
513 \begin{algorithm}
514 \caption{k-Nearest Neighbors}
515 \begin{algorithmic}
516 \label{alg:knn}
517 \REQUIRE{pattern vector $\vec P$, $k > 0$, set of reference players $R$}
518 \FORALL{r $\in$ R }
519 \STATE $D[r] \leftarrow EuclideanDistance(\vec p_r, \vec P)$
520 \ENDFOR
521 \STATE $N \leftarrow SelectSmallest(k, R, D)$
522 \STATE $\vec S \leftarrow \vec 0$
523 \FORALL{r $\in$ N }
524 \STATE $\vec S \leftarrow \vec S + Weight(D[r]) * \vec s_r $
525 \ENDFOR
526 \end{algorithmic}
527 \end{algorithm}
529 \subsection{Neural Network Classifier}
532 \subsection{Implementation}
535 We have implemented the data mining methods as an open-source project
536 ``gostyle'' (TODO). TODO.
537 PCA: In our implementation, we use a~library called MDP \cite{MDP}.
540 \section{Style Components Analysis}
543 \section{Strength Estimation Analysis}
546 \section{Proposed Applications}
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612 %% Some packages, such as MDW tools, offer better commands for making tables
613 %% than the plain LaTeX2e tabular which is used here.
614 %\begin{tabular}{|c||c|}
615 %\hline
616 %One & Two\\
617 %\hline
618 %Three & Four\\
619 %\hline
620 %\end{tabular}
621 %\end{table}
624 % Note that IEEE does not put floats in the very first column - or typically
625 % anywhere on the first page for that matter. Also, in-text middle ("here")
626 % positioning is not used. Most IEEE journals use top floats exclusively.
627 % Note that, LaTeX2e, unlike IEEE journals, places footnotes above bottom
628 % floats. This can be corrected via the \fnbelowfloat command of the
629 % stfloats package.
633 \section{Conclusion}
634 The conclusion goes here.
635 We have shown brm and proposed brm.
637 Future research might explore
638 Sparse PCA
644 % if have a single appendix:
645 %\appendix[Proof of the Zonklar Equations]
646 % or
647 %\appendix % for no appendix heading
648 % do not use \section anymore after \appendix, only \section*
649 % is possibly needed
651 % use appendices with more than one appendix
652 % then use \section to start each appendix
653 % you must declare a \section before using any
654 % \subsection or using \label (\appendices by itself
655 % starts a section numbered zero.)
659 %\appendices
660 %\section{Proof of the First Zonklar Equation}
661 %Appendix one text goes here.
663 %% you can choose not to have a title for an appendix
664 %% if you want by leaving the argument blank
665 %\section{}
666 %Appendix two text goes here.
669 % use section* for acknowledgement
670 \section*{Acknowledgment}
671 \label{acknowledgement}
674 The authors would like to thank...
677 % Can use something like this to put references on a page
678 % by themselves when using endfloat and the captionsoff option.
679 \ifCLASSOPTIONcaptionsoff
680 \newpage
685 % trigger a \newpage just before the given reference
686 % number - used to balance the columns on the last page
687 % adjust value as needed - may need to be readjusted if
688 % the document is modified later
689 %\IEEEtriggeratref{8}
690 % The "triggered" command can be changed if desired:
691 %\IEEEtriggercmd{\enlargethispage{-5in}}
693 % references section
695 % can use a bibliography generated by BibTeX as a .bbl file
696 % BibTeX documentation can be easily obtained at:
697 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
698 % The IEEEtran BibTeX style support page is at:
699 % http://www.michaelshell.org/tex/ieeetran/bibtex/
700 \bibliographystyle{IEEEtran}
701 % argument is your BibTeX string definitions and bibliography database(s)
702 \bibliography{gostyle}
704 % <OR> manually copy in the resultant .bbl file
705 % set second argument of \begin to the number of references
706 % (used to reserve space for the reference number labels box)
707 %\begin{thebibliography}{1}
709 %\bibitem{MasterMCTS}
711 %\end{thebibliography}
713 % biography section
715 % If you have an EPS/PDF photo (graphicx package needed) extra braces are
716 % needed around the contents of the optional argument to biography to prevent
717 % the LaTeX parser from getting confused when it sees the complicated
718 % \includegraphics command within an optional argument. (You could create
719 % your own custom macro containing the \includegraphics command to make things
720 % simpler here.)
721 %\begin{biography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
722 % or if you just want to reserve a space for a photo:
724 \begin{IEEEbiography}{Michael Shell}
725 Biography text here.
726 \end{IEEEbiography}
728 % if you will not have a photo at all:
729 \begin{IEEEbiographynophoto}{John Doe}
730 Biography text here.
731 \end{IEEEbiographynophoto}
733 % insert where needed to balance the two columns on the last page with
734 % biographies
735 %\newpage
737 \begin{IEEEbiographynophoto}{Jane Doe}
738 Biography text here.
739 \end{IEEEbiographynophoto}
741 % You can push biographies down or up by placing
742 % a \vfill before or after them. The appropriate
743 % use of \vfill depends on what kind of text is
744 % on the last page and whether or not the columns
745 % are being equalized.
747 %\vfill
749 % Can be used to pull up biographies so that the bottom of the last one
750 % is flush with the other column.
751 %\enlargethispage{-5in}
755 % that's all folks
756 \end{document}