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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".

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295 board games, go, data mining, player strength, playing style

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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

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.

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

368 being well-known within the community 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

376 as shown in the table below.

379 \noindent

380 %\begin{table}

382 %\caption{Styles}

384 \hline

387 Territoriality & Moyo & Territorial \\

388 Orthodoxity & Classic & Novel \\

389 Aggressivity & Calm & Figting \\

390 Thickness & Safe & Shinogi \\ \hline

393 %\end{table}

396 Averaging this expert based evaluation yields

400 %-- each with a \emph{pattern vector} $\vec p_i$ and \emph{style vector} $\vec s_i$.

404 In addition to the explicit expert knowledge, we use the data obtained by...

406 TODO rozvest uvod, nemuze se zacinat jenom As the input...

409 use the SGF format (TODO) in our implementation.} organized by player names.

411 professional games, dating from the early Go history 1500 years ago to the present.

412 We use this collection for style analysis and detailed correlation analysis

413 of well-known Go professionals.

414 The other source is Go Teaching Ladder reviews (TODO). These include 7600 games

415 of players spanning over all strength levels; we use this collection

416 for finding correlations between moves of players of the same strength rank.

418 In order to generate the required compact description of most frequently played moves,

421 For each player, we then count how many times was each of those $n$ patterns played

422 during all his games and finally assign him a~{\em pattern vector} $\vec p$ of dimension $n$, with each

423 dimension corresponding to the relative number of occurences of a given pattern

424 (with respect to player's most played \emph{top pattern}). Using relative numbers of occurences ensures that

426 therefore even players with different number of games in the database have comparable \emph{pattern vectors}.

429 We need to define how to compose the patterns we use to describe moves.

430 There are some tradeoffs in play - overly general descriptions carry too few

431 information to discern various player attributes; too specific descriptions

432 gather too few specimen over the games sample and the vector differences are

433 not statistically significant.

435 We have chosen an intuitive and simple approach inspired by pattern features

436 used when computing ELO ratings for candidate patterns in Computer Go play.

438 (name-value pairs) matched at the position of the played move.

439 We use these features:

442 \item capture move flag

443 \item atari move flag

444 \item atari escape flag

445 \item contiguity-to-last flag --- whether the move has been played in one of 8 neighbors of the last move

446 \item contiguity-to-second-last flag

448 \item spatial pattern --- configuration of stones around the played move

451 The spatial patterns are normalized (using a dictionary) to be always

452 black-to-play and maintain translational and rotational symmetry.

457 are matched.

461 We have implemented the data extraction by making use of the pattern

462 features matching implementation within the Pachi go-playing program

463 (TODO). We extract information on players by converting the SGF game

465 engine which outputs a~single patternspec per move. We can then gather

466 all encountered patternspecs belonging to a~given player and summarize

467 them; the $\vec p$ vector then consists of normalized counts of

468 the given $n$ most frequent patternspecs.

474 To assess the properties of gathered \emph{pattern vectors} and their influence on playing styles,

475 we have analysed the data by a~few basic data minining techniques.

477 First two methods rely purely on data gathered from the GoGoD database. Principal component

478 analysis finds orthogonal vector components that have biggest variance. Reversing the process then

479 indicates which patterns correlate with each style. Additionally, PCA can be used as a vector-preprocessing

482 A~second method -- Kohonen's networks -- is based on the theory of self-organizing maps of neurons that

483 compete against each other for representation of the input space. Because neurons in the network are

484 organized in a two-dimensional plane, the trained network virtually spreads vectors to the 2D plane,

485 allowing for simple visualization.

487 In addition to methods operating just upon the set of \emph{pattern vectors}, we have used and compared two methods

488 that approximate an unknown \emph{style vector} $\vec S$ of a player with known \emph{pattern vector} $\vec P$.

490 First of them is called $k$-Nearest Neighbor (kNN) classification.

491 Simpy said kNN approximates $\vec S$ by the ``average'' of \emph{style vectors} of $k$ nearest \emph{pattern vectors}.

492 The last method is based on the theory of Neural Networks -- networks of artificial neurons, that are used

493 for their generalization abilities. Neural network can learn correlations between input and output vectors and

494 generalize the ``knowledge'' to unknown vectors sufficiently good.

496 TODO rozdelit na algo/results??

500 Principal Component Analysis \emph{PCA} \cite{Jolliffe1986} is a~method we use to reduce the dimensions of

503 Shortly, PCA is an eigenvalue decomposition of a~covariance matrix of centered \emph{pattern vectors}.

504 It can be thought of as a~mapping $o$ from $n$-dimensional vector space to a~reduced $m$-dimensional vector space.

505 The base of this reduced vector space comprises $m$ eigenvectors of original vectors' covariance matrix.

506 We choose them to be the eigenvectors with biggest eigenvalues.

507 Ordered by decreasing eigenvalues, the eigenvectors form rows of the transformation matrix $W$.

509 Finally, we represent reduced \emph{pattern vectors} as a vector of coeficients of this eigenvector-base.

510 For each original \emph{pattern vector} $\vec p_i$, we obtain its new representation $\vec r_i$ as shown

511 in the following equation:

526 \ENDFOR

529 \ENDFOR

531 \STATE Get $m$ biggest eigenvalues

532 \STATE According eigenvectors ordered by decreasing eigenvalues form rows of matrix $W$

535 \ENDFOR

541 Kohonen map is a self-organizing network with neurons organized in a two-dimensional plane.

542 Neurons in the map compete for representation of input vector space. Each neuron $\vec n$ represents a vector

543 and the network is trained so that the neurons that are topologically close tend to represent vectors that

544 are close as well. That is realised as follows. Initially random network is sequentially trained;

545 in each iterations we choose a random training vector $\vec t$ and find neuron $\vec w$ that is closest

548 We then adapt neurons from the neighbourhood of $\vec w$ employing an equation:

552 where $\alpha$ is a learning parameter, usually decreasing in time. $Influence()$ is a function that forces neurons

553 to spread. Such function is usually realised using a mexican hat function or a difference-of-gaussians (see \cite{TODO}

554 for details). A state of the network can be valued by calculating mean square difference between each $\vec t \in T$

568 \REPEAT

573 \ENDFOR

576 \STATE $\vec n \leftarrow \vec n + \alpha(It) \cdot \mathit{Influence}(\vec w, \vec n) \cdot ( \vec t - \vec n ) $

577 \ENDFOR

585 K-nearest neigbors is an essential classification technique.

586 We use it to approximate player's \emph{style vector} $\vec S$, assuming that his \emph{pattern vector} $\vec P$ is known.

594 Note that the weight is a function of distance and it is not explicitly defined in Algorithm \ref{alg:knn}.

595 During our research, exponentialy decreasing weight has proven to be sufficient.

604 \ENDFOR

609 \ENDFOR

618 Neural networks (NN) are known for their ability to generalize and find correlations and patterns between

619 input and output data. Neural network is an adaptive system and it

620 must undergo a certain training before it can be reasonably used. Basically, we use

625 Technically, neural network is a network of interconnected computational units called neurons.

626 A feedforward neural network has a layered topology; it usually has one \emph{input layer}, one \emph{output

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

631 The computation proceeds in a discrete time steps.

632 In the first step, \emph{activation} of neurons in the \emph{input layer} is set according to the \emph{input vector}.

633 Then, we iteratively compute output of each neuron in next layer until the output layer is reached. The activity of

634 output layer is then presented as a result.

636 The activation $y_i$ of neuron $i$ from the layer $I$ is computed using the following equation:

640 where $J$ is a previous layer, while $y_j$ is the activation for neurons from $J$ layer. Function $f()$ is

641 called \emph{activation function} and its purpose is to bound outputs of neurons. A typical example of an activation

642 function is a sigmoid function.\footnote{The sigmoid function is a special case of the logistic function; it is defined by the formula

643 $\sigma(x)=\frac{1}{1+e^{-(rx+k)}}$, parameters control the growth rate ($r$) and the x-position ($k$).}

646 The training of the feedforward neural network usually involves some

650 Because the \emph{reference set} is not usually very large, we have devised a simple method for its extension.

651 This enhancement is based upon adding random linear combinations of \emph{style and pattern vectors} to the training set.

653 As insinuated above, the training set consist of pairs of input vectors (\emph{pattern vectors}) and

654 desired output vectors (\emph{style vectors}). The training set $T$ is then enlarged by adding linear combinations:

659 T_\mathit{ext} = \{(\vec p, \vec s) | \exists D \subseteq R : \vec p = \sum_{d \in D}{g_d \vec p_d}, \vec s = \sum_{d \in D}{g_d \vec s_d}\}

661 TODO zabudovat $g_d$ dovnitr?

662 where $g_d, d \in D$ are random coeficients, so that $\sum_{d \in D}{g_d} = 1$. The training set

663 is then constructed as:

677 \REPEAT

681 %\FORALL{$(\overrightarrow{Input}, \overrightarrow{DesiredOutput}) \in T$}

682 %\STATE $\overrightarrow{Output} \leftarrow Result(N, \overrightarrow{Input})$

683 %\STATE $E \leftarrow |\overrightarrow{DesiredOutput} - \overrightarrow{Output}|$

689 \ENDFOR

697 TODO num layers, num neurons, ..

703 licensed under GNU GPL.

705 TODO libfann

710 PCA analysis yielded X, chi-square test blabla...

712 We then tried to apply the NN classifier with linear output function on the dataset

713 and that yielded Y (see fig. Z), with MSE abcd.

718 PCA analysis yielded X, chi-square test...

720 We then tried to apply the NN classifier with linear output function on the dataset

721 and that yielded Y (see fig. Z), with MSE abcd.

726 We believe that our findings might be useful for many applications

727 in the area of Go support software as well as Go-playing computer engines.

729 The style analysis can be an excellent teaching aid --- classifying style

730 dimensions based on player's pattern vector, many study recommendations

731 can be given, e.g. about the professional games to replay, the goal being

732 balancing understanding of various styles to achieve well-rounded skill set.

733 This was also our original aim when starting the research and a user-friendly

734 tool based on our work is now being created.

736 We hope that more strong players will look into the style dimensions found

737 by our statistical analysis --- analysis of most played patterns of prospective

738 opponents might prepare for the game, but we especially hope that new insights

739 on strategic purposes of various shapes and general human understanding

740 of the game might be achieved by investigating the style-specific patterns.

742 Classifying playing strength of a pattern vector of a player can be used

743 e.g. to help determine initial real-world rating of a player before their

744 first tournament based on games played on the internet; some players especially

745 in less populated areas could get fairly strong before playing their first

746 real tournament.

748 Analysis of pattern vectors extracted from games of Go-playing programs

749 in light of the shown strength and style distributions might help to

750 highlight some weaknesses and room for improvements. (However, since

751 correlation does not imply causation, simply optimizing Go-playing programs

752 according to these vectors is unlikely to yield good results.)

753 Another interesting applications in Go-playing programs might be strength

754 adjustment; the program can classify the player's level based on the pattern

755 vector from its previous games and auto-adjust its difficulty settings

756 accordingly to provide more even games for beginners.

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774 %\includegraphics[width=2.5in]{myfigure}

775 % where an .eps filename suffix will be assumed under latex,

776 % and a .pdf suffix will be assumed for pdflatex; or what has been declared

777 % via \DeclareGraphicsExtensions.

778 %\caption{Simulation Results}

779 %\label{fig_sim}

780 %\end{figure}

782 % Note that IEEE typically puts floats only at the top, even when this

783 % results in a large percentage of a column being occupied by floats.

786 % An example of a double column floating figure using two subfigures.

787 % (The subfig.sty package must be loaded for this to work.)

788 % The subfigure \label commands are set within each subfloat command, the

789 % \label for the overall figure must come after \caption.

790 % \hfil must be used as a separator to get equal spacing.

791 % The subfigure.sty package works much the same way, except \subfigure is

792 % used instead of \subfloat.

793 %

794 %\begin{figure*}[!t]

795 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%

796 %\label{fig_first_case}}

797 %\hfil

798 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%

799 %\label{fig_second_case}}}

800 %\caption{Simulation results}

801 %\label{fig_sim}

802 %\end{figure*}

803 %

804 % Note that often IEEE papers with subfigures do not employ subfigure

805 % captions (using the optional argument to \subfloat), but instead will

806 % reference/describe all of them (a), (b), etc., within the main caption.

809 % An example of a floating table. Note that, for IEEE style tables, the

810 % \caption command should come BEFORE the table. Table text will default to

811 % \footnotesize as IEEE normally uses this smaller font for tables.

812 % The \label must come after \caption as always.

813 %

814 %\begin{table}[!t]

815 %% increase table row spacing, adjust to taste

816 %\renewcommand{\arraystretch}{1.3}

817 % if using array.sty, it might be a good idea to tweak the value of

818 % \extrarowheight as needed to properly center the text within the cells

819 %\caption{An Example of a Table}

820 %\label{table_example}

821 %\centering

822 %% Some packages, such as MDW tools, offer better commands for making tables

823 %% than the plain LaTeX2e tabular which is used here.

824 %\begin{tabular}{|c||c|}

825 %\hline

826 %One & Two\\

827 %\hline

828 %Three & Four\\

829 %\hline

830 %\end{tabular}

831 %\end{table}

834 % Note that IEEE does not put floats in the very first column - or typically

835 % anywhere on the first page for that matter. Also, in-text middle ("here")

836 % positioning is not used. Most IEEE journals use top floats exclusively.

837 % Note that, LaTeX2e, unlike IEEE journals, places footnotes above bottom

838 % floats. This can be corrected via the \fnbelowfloat command of the

839 % stfloats package.

844 The conclusion goes here.

845 We have shown brm and proposed brm.

847 Since we are not aware of any previous research on this topic and we

848 are limited by space and time constraints, plenty of research remains

849 to be done. There is plenty of room for further research in all parts

850 of our analysis --- different methods of generating the $\vec p$ vectors

851 can be explored; other data mining methods could be tried.

852 It can be argued that many players adjust their style by game conditions

853 (Go development era, handicap, komi and color, time limits, opponent)

854 or styles might express differently in various game stages.

855 More professional players could be consulted on the findings

856 and for style scales calibration. Impact of handicap games on by-strength

857 $\vec p$ distribution should be investigated.

859 TODO: Future research --- Sparse PCA

864 % if have a single appendix:

865 %\appendix[Proof of the Zonklar Equations]

866 % or

867 %\appendix % for no appendix heading

868 % do not use \section anymore after \appendix, only \section*

869 % is possibly needed

871 % use appendices with more than one appendix

872 % then use \section to start each appendix

873 % you must declare a \section before using any

874 % \subsection or using \label (\appendices by itself

875 % starts a section numbered zero.)

876 %

879 %\appendices

880 %\section{Proof of the First Zonklar Equation}

881 %Appendix one text goes here.

882 %

883 %% you can choose not to have a title for an appendix

884 %% if you want by leaving the argument blank

885 %\section{}

886 %Appendix two text goes here.

889 % use section* for acknowledgement

894 We would like to thank X for reviewing our paper.

895 We appreciate helpful comments on our general methodology

896 by John Fairbairn, T. M. Hall, Robert Jasiek

898 Finally, we are very grateful for ranking of go styles of selected professionals

902 % Can use something like this to put references on a page

903 % by themselves when using endfloat and the captionsoff option.

904 \ifCLASSOPTIONcaptionsoff

905 \newpage

906 \fi

910 % trigger a \newpage just before the given reference

911 % number - used to balance the columns on the last page

912 % adjust value as needed - may need to be readjusted if

913 % the document is modified later

914 %\IEEEtriggeratref{8}

915 % The "triggered" command can be changed if desired:

916 %\IEEEtriggercmd{\enlargethispage{-5in}}

918 % references section

920 % can use a bibliography generated by BibTeX as a .bbl file

921 % BibTeX documentation can be easily obtained at:

922 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/

923 % The IEEEtran BibTeX style support page is at:

924 % http://www.michaelshell.org/tex/ieeetran/bibtex/

926 % argument is your BibTeX string definitions and bibliography database(s)

928 %

929 % <OR> manually copy in the resultant .bbl file

930 % set second argument of \begin to the number of references

931 % (used to reserve space for the reference number labels box)

932 %\begin{thebibliography}{1}

933 %

934 %\bibitem{MasterMCTS}

935 %

936 %\end{thebibliography}

938 % biography section

939 %

940 % If you have an EPS/PDF photo (graphicx package needed) extra braces are

941 % needed around the contents of the optional argument to biography to prevent

942 % the LaTeX parser from getting confused when it sees the complicated

943 % \includegraphics command within an optional argument. (You could create

944 % your own custom macro containing the \includegraphics command to make things

945 % simpler here.)

946 %\begin{biography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}

947 % or if you just want to reserve a space for a photo:

950 Biography text here.

953 % if you will not have a photo at all:

955 Biography text here.

958 % insert where needed to balance the two columns on the last page with

959 % biographies

960 %\newpage

963 Biography text here.

966 % You can push biographies down or up by placing

967 % a \vfill before or after them. The appropriate

968 % use of \vfill depends on what kind of text is

969 % on the last page and whether or not the columns

970 % are being equalized.

972 %\vfill

974 % Can be used to pull up biographies so that the bottom of the last one

975 % is flush with the other column.

976 %\enlargethispage{-5in}

980 % that's all folks