tex: several grammar tweaks
[gostyle.git] / tex / gostyle.tex
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200 % to submit to, of course. )
202 % correct bad hyphenation here
203 \hyphenation{op-tical net-works semi-conduc-tor}
206 \begin{document}
208 % paper title
209 % can use linebreaks \\ within to get better formatting as desired
210 \title{On Pattern Feature Trends in Large Go Game Corpus}
212 % use \thanks{} to gain access to the first footnote area
213 % a separate \thanks must be used for each paragraph as LaTeX2e's \thanks
214 % was not built to handle multiple paragraphs
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.}}
219 % note the % following the last \IEEEmembership and also \thanks -
220 % these prevent an unwanted space from occurring between the last author name
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233 % you are supposed to have spaces between the names. For what it is worth,
234 % this is a minor point as most people would not even notice if the said evil
235 % space somehow managed to creep in.
238 % The paper headers
239 \markboth{Transactions on Computational Intelligence and AI in Games}%
240 {On Pattern Feature Trends in Large Go Game Corpus}
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242 % after the title page when using the twoside option.
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254 %\IEEEpubid{0000--0000/00\$00.00~\copyright~2007 IEEE}
255 % Remember, if you use this you must call \IEEEpubidadjcol in the second
256 % column for its text to clear the IEEEpubid mark.
260 % use for special paper notices
261 %\IEEEspecialpapernotice{(Invited Paper)}
266 % make the title area
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}
286 % IEEEtran.cls defaults to using nonbold math in the Abstract.
287 % This preserves the distinction between vectors and scalars. However,
288 % if the journal you are submitting to favors bold math in the abstract,
289 % then you can use LaTeX's standard command \boldmath at the very start
290 % of the abstract to achieve this. Many IEEE journals frown on math
291 % in the abstract anyway.
293 % Note that keywords are not normally used for peerreview papers.
294 \begin{IEEEkeywords}
295 board games, go, data mining, player strength, playing style
296 \end{IEEEkeywords}
303 % For peer review papers, you can put extra information on the cover
304 % page as needed:
305 % \ifCLASSOPTIONpeerreview
306 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
307 % \fi
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310 % creates the second title. It will be ignored for other modes.
311 \IEEEpeerreviewmaketitle
315 \section{Introduction}
316 % The very first letter is a 2 line initial drop letter followed
317 % by the rest of the first word in caps.
319 % form to use if the first word consists of a single letter:
320 % \IEEEPARstart{A}{demo} file is ....
322 % form to use if you need the single drop letter followed by
323 % normal text (unknown if ever used by IEEE):
324 % \IEEEPARstart{A}{}demo file is ....
326 % Some journals put the first two words in caps:
327 % \IEEEPARstart{T}{his demo} file is ....
329 % Here we have the typical use of a "T" for an initial drop letter
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 and assign the player a~vector $\vec p$ describing relative
379 frequency of moves with the same description. These vectors are called \emph{pattern vectors}
380 in the text.
382 TODO: Elaborate, exact construct.
384 \subsection{Pattern Features}
386 \subsection{Expert-based knowledge}
387 \label{style-vectors}
388 Apart from the pattern vectors extracted from game collections, we have gathered some
389 expert-based information about (simplified) traditional-meaning playing styles.
390 We have asked several high-level Go players (see the acknowledgement \ref{acknowledgement})
391 to explicitly evaluate styles for some well-known Go players.
392 \footnote{The well-known Go players were incidentally chosen so that a rich
393 set of their games is present in the GoGoD 2009 collection.}
395 This expert-based knowledge allows us to predict styles of unknown players based on
396 the similarity of their pattern vectors, as well as discover correlations between
397 styles and proportions of played patterns.
399 Experts were asked to assign each of player's style (including territoriality, orthodoxity,
400 aggressivity, thickness) a number on a scale from 1 to 10. These are interpreted
401 as shown in the table below.
403 \vspace{4mm}
404 \noindent
405 %\begin{table}
406 \begin{center}
407 %\caption{Styles}
408 \begin{tabular}{|c|c|c|}
409 \hline
410 \multicolumn{3}{|c|}{Styles} \\ \hline
411 Style & 1 & 10\\ \hline
412 Territoriality & Moyo & Territorial \\
413 Orthodoxity & Classic & Novel \\
414 Aggressivity & Calm & Figting \\
415 Thickness & Safe & Shinogi \\ \hline
416 \end{tabular}
417 \end{center}
418 %\end{table}
420 Averaging and rescaling the expert based evaluation yields a set of
421 \emph{reference style vectors} $\vec s_r$.
422 %-- each with a \emph{pattern vector} $\vec p_i$ and \emph{style vector} $\vec s_i$.
424 \subsection{Implementation}
426 We have implemented the data extraction by making use of the pattern
427 features matching implementation within the Pachi go-playing program
428 (TODO). We extract information on players by converting the SGF game
429 records to GTP (TODO) stream that feeds Pachi's {\tt patternscan}
430 engine which outputs a~single patternspec per move. We can then gather
431 all encountered patternspecs belonging to a~given player and summarize
432 them; the $\vec p$ vector then consists of normalized counts of
433 the given $n$ most frequent patternspecs.
436 \section{Data Mining}
437 To assess the properties of gathered \emph{pattern vectors} and their influence on playing styles,
438 we have analysed the data by a~few basic data minining techniques.
440 TODO PCA: We use it either on it own, or as a~pre-processing making data suitable for other methods.
442 TODO rozdelit na algo/results??
444 \subsection{Principal Component Analysis}
445 Principal Component Analysis \emph{PCA} \cite{Jolliffe1986} is a~method we use to reduce the dimensions of
446 \emph{pattern vectors} while preserving as much information as possible.
448 Shortly, PCA is an eigenvalue decomposition of a~covariance matrix of centered \emph{pattern vectors}.
449 It can be thought of as a~mapping $o$ from $n$-dimensional vector space to a~reduced $m$-dimensional vector space.
450 The base of this reduced vector space comprises $m$ eigenvectors of original vectors' covariance matrix.
451 We choose them to be the eigenvectors with biggest eigenvalues.
452 Ordered by decreasing eigenvalues, the eigenvectors form rows of the transformation matrix $W$.
454 Finally, we represent reduced \emph{pattern vectors} as a vector of coeficients of this eigenvector-base.
455 For each original \emph{pattern vector} $\vec p_i$, we obtain its new representation $\vec r_i$ as shown
456 in the following equation:
457 \begin{equation}
458 \vec r_i = W * \vec p_i
459 \end{equation}
461 The whole process is described in the Algorithm \ref{alg:pca}.
463 \begin{algorithm}
464 \caption{PCA -- Principal Component analysis}
465 \begin{algorithmic}[1]
466 \label{alg:pca}
467 \REQUIRE{$m > 0$, set of players $R$ with \emph{pattern vectors} $p_r$}
468 \STATE $\vec \mu \leftarrow 1/|R| * \sum_{r \in R}{\vec p_r}$
469 \FOR{ $r \in R$}
470 \STATE $\vec p_r \leftarrow \vec p_r - \vec \mu$
472 \FOR{ $(i,j) \in \{1,... ,n\} \times \{1,... ,n\}$}
473 \STATE $Cov[i,j] \leftarrow 1/|R| * \sum_{r \in R}{\vec p_{ri} * \vec p_{rj}}$
475 \STATE Compute Eigenvalue Decomposition of $Cov$ matrix
476 \STATE Get $m$ biggest eigenvalues
477 \STATE According eigenvectors ordered by decreasing eigenvalues form rows of matrix $W$
478 \FOR{ $r \in R$}
479 \STATE $\vec r_r\leftarrow W \vec p_r$
481 \end{algorithmic}
482 \end{algorithm}
484 \subsection{?? Kohonen Maps ??}
486 \subsection{k-nearest Neighbors Classifier}
487 K-nearest neigbors is an essential classification technique.
488 We use it to approximate player's \emph{style vector} $\vec S$, assuming that his \emph{pattern vector} $\vec P$ is known.
489 To achieve this, we utilize \emph{reference style vectors} (see section \ref{style-vectors}).
491 The idea is based on a assumption that similarities in players' \emph{pattern vectors}
492 correlate with similarities in players' \emph{style vectors}. We try to approximate $\vec S$
493 as a weighted average of \emph{style vectors}
494 $\vec s_i$ of $k$ players with \emph{pattern vectors} $\vec p_i$ closest to $\vec P$.
495 This is illustrated in the Algorithm \ref{alg:knn}.
496 Note that the weight is a function of distance and it is not explicitly defined in Algorithm \ref{alg:knn}.
497 During our research, exponentialy decreasing weight has proven to be sufficient.
499 \begin{algorithm}
500 \caption{k-Nearest Neighbors}
501 \begin{algorithmic}
502 \label{alg:knn}
503 \REQUIRE{pattern vector $\vec P$, $k > 0$, set of reference players $R$}
504 \FORALL{r $\in$ R }
505 \STATE $D[r] \leftarrow EuclideanDistance(\vec p_r, \vec P)$
507 \STATE $N \leftarrow SelectSmallest(k, R, D)$
508 \STATE $\vec S \leftarrow \vec 0$
509 \FORALL{r $\in$ N }
510 \STATE $\vec S \leftarrow \vec S + Weight(D[r]) * \vec s_r $
512 \end{algorithmic}
513 \end{algorithm}
515 \subsection{Neural Network Classifier}
518 \subsection{Implementation}
521 We have implemented the data mining methods as an open-source project
522 ``gostyle'' (TODO). TODO.
523 PCA: In our implementation, we use a~library called MDP \cite{MDP}.
526 \section{Style Components Analysis}
529 \section{Strength Estimation Analysis}
532 \section{Proposed Applications}
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570 %\begin{figure*}[!t]
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572 %\label{fig_first_case}}
573 %\hfil
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619 \section{Conclusion}
620 The conclusion goes here.
621 We have shown brm and proposed brm.
623 Future research might explore
624 Sparse PCA
630 % if have a single appendix:
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637 % use appendices with more than one appendix
638 % then use \section to start each appendix
639 % you must declare a \section before using any
640 % \subsection or using \label (\appendices by itself
641 % starts a section numbered zero.)
645 %\appendices
646 %\section{Proof of the First Zonklar Equation}
647 %Appendix one text goes here.
649 %% you can choose not to have a title for an appendix
650 %% if you want by leaving the argument blank
651 %\section{}
652 %Appendix two text goes here.
655 % use section* for acknowledgement
656 \section*{Acknowledgment}
657 \label{acknowledgement}
660 The authors would like to thank...
663 % Can use something like this to put references on a page
664 % by themselves when using endfloat and the captionsoff option.
665 \ifCLASSOPTIONcaptionsoff
666 \newpage
671 % trigger a \newpage just before the given reference
672 % number - used to balance the columns on the last page
673 % adjust value as needed - may need to be readjusted if
674 % the document is modified later
675 %\IEEEtriggeratref{8}
676 % The "triggered" command can be changed if desired:
677 %\IEEEtriggercmd{\enlargethispage{-5in}}
679 % references section
681 % can use a bibliography generated by BibTeX as a .bbl file
682 % BibTeX documentation can be easily obtained at:
683 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
684 % The IEEEtran BibTeX style support page is at:
685 % http://www.michaelshell.org/tex/ieeetran/bibtex/
686 \bibliographystyle{IEEEtran}
687 % argument is your BibTeX string definitions and bibliography database(s)
688 \bibliography{gostyle}
690 % <OR> manually copy in the resultant .bbl file
691 % set second argument of \begin to the number of references
692 % (used to reserve space for the reference number labels box)
693 %\begin{thebibliography}{1}
695 %\bibitem{MasterMCTS}
697 %\end{thebibliography}
699 % biography section
701 % If you have an EPS/PDF photo (graphicx package needed) extra braces are
702 % needed around the contents of the optional argument to biography to prevent
703 % the LaTeX parser from getting confused when it sees the complicated
704 % \includegraphics command within an optional argument. (You could create
705 % your own custom macro containing the \includegraphics command to make things
706 % simpler here.)
707 %\begin{biography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
708 % or if you just want to reserve a space for a photo:
710 \begin{IEEEbiography}{Michael Shell}
711 Biography text here.
712 \end{IEEEbiography}
714 % if you will not have a photo at all:
715 \begin{IEEEbiographynophoto}{John Doe}
716 Biography text here.
717 \end{IEEEbiographynophoto}
719 % insert where needed to balance the two columns on the last page with
720 % biographies
721 %\newpage
723 \begin{IEEEbiographynophoto}{Jane Doe}
724 Biography text here.
725 \end{IEEEbiographynophoto}
727 % You can push biographies down or up by placing
728 % a \vfill before or after them. The appropriate
729 % use of \vfill depends on what kind of text is
730 % on the last page and whether or not the columns
731 % are being equalized.
733 %\vfill
735 % Can be used to pull up biographies so that the bottom of the last one
736 % is flush with the other column.
737 %\enlargethispage{-5in}
741 % that's all folks
742 \end{document}