tex: Expert-based knowledge - wording changes etc.
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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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267 \maketitle
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{Expert-based knowledge}
361 \label{style-vectors}
362 In order to provide a reference frame for our style analysis,
363 we have gathered some expert-based information about various
364 traditionally perceived style aspects.
365 Three high-level Go players (Alexander Dinerstein 3-pro, Motoki Noguchi
366 7-dan and Vit Brunner 4-dan) have judged style of several Go
367 professionals (chosen for both being well-known within the community
368 and having large number of played games in our collection).
370 This expert-based knowledge allows us to predict styles of unknown players based on
371 the similarity of their pattern vectors, as well as discover correlations between
372 styles and proportions of played patterns.
374 Experts were asked to assign each of player's style a number
375 on a scale from 1 to 10. These are interpreted
376 as shown in the table below.
378 \vspace{4mm}
379 \noindent
380 %\begin{table}
381 \begin{center}
382 %\caption{Styles}
383 \begin{tabular}{|c|c|c|}
384 \hline
385 \multicolumn{3}{|c|}{Styles} \\ \hline
386 Style & 1 & 10\\ \hline
387 Territoriality & Moyo & Territorial \\
388 Orthodoxity & Classic & Novel \\
389 Aggressivity & Calm & Figting \\
390 Thickness & Safe & Shinogi \\ \hline
391 \end{tabular}
392 \end{center}
393 %\end{table}
395 Averaging and rescaling the expert based evaluation yields a set of
396 \emph{reference style vectors} $\vec s_r$.
397 %-- each with a \emph{pattern vector} $\vec p_i$ and \emph{style vector} $\vec s_i$.
400 \section{Data Extraction}
401 \label{pattern-vectors}
403 As the input of our method, we assume a~collection of game records\footnote{We
404 use the SGF format (TODO) in our implementation.} organized by player names.
405 We use two collections; the first one is GoGoD Winter 2009 (TODO) containing 42000 (TODO)
406 professional games, dating from the early Go history 1500 years ago to the present.
407 We use this collection for style analysis and detailed correlation analysis
408 of well-known Go professionals.
409 The other source is Go Teaching Ladder reviews (TODO). These include 7600 games
410 of players spanning over all strength levels; we use this collection
411 for finding correlations between moves of players of the same strength rank.
413 In order to generate the required compact description of most played moves,
414 for each player, we extract a~generic description from each move
415 played by the player, then take the most occuring $n$ patterns across all players%
416 \footnote{We use $n=500$ in our analysis.} and assign each player a~{\em pattern vector}
417 $\vec d$ where each dimension corresponds to the number of occurences of
418 one given pattern normalized to range $[0,1]$.
420 \subsection{Pattern Features}
422 Of course a big question is how to compose the pattern descriptions.
423 There are some tradeoffs in play - overly general descriptions carry too few
424 information to discern various player attributes; too specific descriptions
425 gather too few specimen over the games and the differences in vectors are
426 not statistically significant.
428 We have chosen an intuitive and simple approach inspired by pattern features
429 used when computing ELO ratings for candidate patterns in Computer Go play.
430 \cite{ELO} Each pattern is combination of several {\em pattern features}
431 matched at the position of the played move. We use these features:
433 \begin{itemize}
434 \item TODO
435 \end{itemize}
437 \subsection{Implementation}
439 We have implemented the data extraction by making use of the pattern
440 features matching implementation within the Pachi go-playing program
441 (TODO). We extract information on players by converting the SGF game
442 records to GTP (TODO) stream that feeds Pachi's {\tt patternscan}
443 engine which outputs a~single patternspec per move. We can then gather
444 all encountered patternspecs belonging to a~given player and summarize
445 them; the $\vec p$ vector then consists of normalized counts of
446 the given $n$ most frequent patternspecs.
449 \section{Data Mining}
450 To assess the properties of gathered \emph{pattern vectors} and their influence on playing styles,
451 we have analysed the data by a~few basic data minining techniques.
453 TODO PCA: We use it either on it own, or as a~pre-processing making data suitable for other methods.
455 TODO rozdelit na algo/results??
457 \subsection{Principal Component Analysis}
458 Principal Component Analysis \emph{PCA} \cite{Jolliffe1986} is a~method we use to reduce the dimensions of
459 \emph{pattern vectors} while preserving as much information as possible.
461 Shortly, PCA is an eigenvalue decomposition of a~covariance matrix of centered \emph{pattern vectors}.
462 It can be thought of as a~mapping $o$ from $n$-dimensional vector space to a~reduced $m$-dimensional vector space.
463 The base of this reduced vector space comprises $m$ eigenvectors of original vectors' covariance matrix.
464 We choose them to be the eigenvectors with biggest eigenvalues.
465 Ordered by decreasing eigenvalues, the eigenvectors form rows of the transformation matrix $W$.
467 Finally, we represent reduced \emph{pattern vectors} as a vector of coeficients of this eigenvector-base.
468 For each original \emph{pattern vector} $\vec p_i$, we obtain its new representation $\vec r_i$ as shown
469 in the following equation:
470 \begin{equation}
471 \vec r_i = W * \vec p_i
472 \end{equation}
474 The whole process is described in the Algorithm \ref{alg:pca}.
476 \begin{algorithm}
477 \caption{PCA -- Principal Component analysis}
478 \begin{algorithmic}[1]
479 \label{alg:pca}
480 \REQUIRE{$m > 0$, set of players $R$ with \emph{pattern vectors} $p_r$}
481 \STATE $\vec \mu \leftarrow 1/|R| * \sum_{r \in R}{\vec p_r}$
482 \FOR{ $r \in R$}
483 \STATE $\vec p_r \leftarrow \vec p_r - \vec \mu$
484 \ENDFOR
485 \FOR{ $(i,j) \in \{1,... ,n\} \times \{1,... ,n\}$}
486 \STATE $Cov[i,j] \leftarrow 1/|R| * \sum_{r \in R}{\vec p_{ri} * \vec p_{rj}}$
487 \ENDFOR
488 \STATE Compute Eigenvalue Decomposition of $Cov$ matrix
489 \STATE Get $m$ biggest eigenvalues
490 \STATE According eigenvectors ordered by decreasing eigenvalues form rows of matrix $W$
491 \FOR{ $r \in R$}
492 \STATE $\vec r_r\leftarrow W \vec p_r$
493 \ENDFOR
494 \end{algorithmic}
495 \end{algorithm}
497 \subsection{?? Kohonen Maps ??}
499 \subsection{k-nearest Neighbors Classifier}
500 K-nearest neigbors is an essential classification technique.
501 We use it to approximate player's \emph{style vector} $\vec S$, assuming that his \emph{pattern vector} $\vec P$ is known.
502 To achieve this, we utilize \emph{reference style vectors} (see section \ref{style-vectors}).
504 The idea is based on a assumption that similarities in players' \emph{pattern vectors}
505 correlate with similarities in players' \emph{style vectors}. We try to approximate $\vec S$
506 as a weighted average of \emph{style vectors}
507 $\vec s_i$ of $k$ players with \emph{pattern vectors} $\vec p_i$ closest to $\vec P$.
508 This is illustrated in the Algorithm \ref{alg:knn}.
509 Note that the weight is a function of distance and it is not explicitly defined in Algorithm \ref{alg:knn}.
510 During our research, exponentialy decreasing weight has proven to be sufficient.
512 \begin{algorithm}
513 \caption{k-Nearest Neighbors}
514 \begin{algorithmic}
515 \label{alg:knn}
516 \REQUIRE{pattern vector $\vec P$, $k > 0$, set of reference players $R$}
517 \FORALL{r $\in$ R }
518 \STATE $D[r] \leftarrow EuclideanDistance(\vec p_r, \vec P)$
519 \ENDFOR
520 \STATE $N \leftarrow SelectSmallest(k, R, D)$
521 \STATE $\vec S \leftarrow \vec 0$
522 \FORALL{r $\in$ N }
523 \STATE $\vec S \leftarrow \vec S + Weight(D[r]) * \vec s_r $
524 \ENDFOR
525 \end{algorithmic}
526 \end{algorithm}
528 \subsection{Neural Network Classifier}
531 \subsection{Implementation}
534 We have implemented the data mining methods as an open-source project
535 ``gostyle'' (TODO). TODO.
536 PCA: In our implementation, we use a~library called MDP \cite{MDP}.
539 \section{Style Components Analysis}
542 \section{Strength Estimation Analysis}
545 \section{Proposed Applications}
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617 %Three & Four\\
618 %\hline
619 %\end{tabular}
620 %\end{table}
623 % Note that IEEE does not put floats in the very first column - or typically
624 % anywhere on the first page for that matter. Also, in-text middle ("here")
625 % positioning is not used. Most IEEE journals use top floats exclusively.
626 % Note that, LaTeX2e, unlike IEEE journals, places footnotes above bottom
627 % floats. This can be corrected via the \fnbelowfloat command of the
628 % stfloats package.
632 \section{Conclusion}
633 The conclusion goes here.
634 We have shown brm and proposed brm.
636 Since we are not aware of any previous research on this topic and we
637 are limited by space and time constraints, plenty of research remains
638 to be done. There is plenty of room for further research in all parts
639 of our analysis --- different methods of generating the $\vec d$ vectors
640 can be explored; other data mining methods could be tried.
641 It can be argued that many players adjust their style by game conditions
642 (Go development era, handicap, komi and color, time limits, opponent)
643 or styles might express differently in various game stages.
644 Finally, more professional players could be consulted on the findings
645 and for style scales calibration.
647 TODO: Future research --- Sparse PCA
652 % if have a single appendix:
653 %\appendix[Proof of the Zonklar Equations]
654 % or
655 %\appendix % for no appendix heading
656 % do not use \section anymore after \appendix, only \section*
657 % is possibly needed
659 % use appendices with more than one appendix
660 % then use \section to start each appendix
661 % you must declare a \section before using any
662 % \subsection or using \label (\appendices by itself
663 % starts a section numbered zero.)
667 %\appendices
668 %\section{Proof of the First Zonklar Equation}
669 %Appendix one text goes here.
671 %% you can choose not to have a title for an appendix
672 %% if you want by leaving the argument blank
673 %\section{}
674 %Appendix two text goes here.
677 % use section* for acknowledgement
678 \section*{Acknowledgment}
679 \label{acknowledgement}
682 We would like to thank X for reviewing our paper.
683 We appreciate helpful comments on our general methodology
684 by John Fairbairn, T. M. Hall, Robert Jasiek
685 and several GoDiscussions.com users. \cite{GoDiscThread}
686 Finally, we are very grateful for ranking of go styles of selected professionals
687 by Alexander Dinerstein 3-pro, Motoki Noguchi TODO and Vit Brunner 4-dan.
690 % Can use something like this to put references on a page
691 % by themselves when using endfloat and the captionsoff option.
692 \ifCLASSOPTIONcaptionsoff
693 \newpage
698 % trigger a \newpage just before the given reference
699 % number - used to balance the columns on the last page
700 % adjust value as needed - may need to be readjusted if
701 % the document is modified later
702 %\IEEEtriggeratref{8}
703 % The "triggered" command can be changed if desired:
704 %\IEEEtriggercmd{\enlargethispage{-5in}}
706 % references section
708 % can use a bibliography generated by BibTeX as a .bbl file
709 % BibTeX documentation can be easily obtained at:
710 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
711 % The IEEEtran BibTeX style support page is at:
712 % http://www.michaelshell.org/tex/ieeetran/bibtex/
713 \bibliographystyle{IEEEtran}
714 % argument is your BibTeX string definitions and bibliography database(s)
715 \bibliography{gostyle}
717 % <OR> manually copy in the resultant .bbl file
718 % set second argument of \begin to the number of references
719 % (used to reserve space for the reference number labels box)
720 %\begin{thebibliography}{1}
722 %\bibitem{MasterMCTS}
724 %\end{thebibliography}
726 % biography section
728 % If you have an EPS/PDF photo (graphicx package needed) extra braces are
729 % needed around the contents of the optional argument to biography to prevent
730 % the LaTeX parser from getting confused when it sees the complicated
731 % \includegraphics command within an optional argument. (You could create
732 % your own custom macro containing the \includegraphics command to make things
733 % simpler here.)
734 %\begin{biography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
735 % or if you just want to reserve a space for a photo:
737 \begin{IEEEbiography}{Michael Shell}
738 Biography text here.
739 \end{IEEEbiography}
741 % if you will not have a photo at all:
742 \begin{IEEEbiographynophoto}{John Doe}
743 Biography text here.
744 \end{IEEEbiographynophoto}
746 % insert where needed to balance the two columns on the last page with
747 % biographies
748 %\newpage
750 \begin{IEEEbiographynophoto}{Jane Doe}
751 Biography text here.
752 \end{IEEEbiographynophoto}
754 % You can push biographies down or up by placing
755 % a \vfill before or after them. The appropriate
756 % use of \vfill depends on what kind of text is
757 % on the last page and whether or not the columns
758 % are being equalized.
760 %\vfill
762 % Can be used to pull up biographies so that the bottom of the last one
763 % is flush with the other column.
764 %\enlargethispage{-5in}
768 % that's all folks
769 \end{document}