tex: Move expert-base knowledge info to latter sections
[gostyle.git] / tex / gostyle.tex
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203 \hyphenation{op-tical net-works semi-conduc-tor}
206 \begin{document}
208 % paper title
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210 \title{On Move Pattern Trends\\in Large Go Games Corpus}
212 % use \thanks{} to gain access to the first footnote area
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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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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}
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293 % Note that keywords are not normally used for peerreview papers.
294 \begin{IEEEkeywords}
295 board games, go, data mining, pattern recongition, 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 \label{pattern-vectors}
362 In addition to the explicit expert knowledge, we use the data obtained by...
364 TODO rozvest uvod, nemuze se zacinat jenom As the input...
366 As the input, we assume a~collection of game records\footnote{We
367 use the SGF format (TODO) in our implementation.} organized by player names.
369 In order to generate the required compact description of most frequently played moves,
370 we construct a set of $n$ most occuring patterns (\emph{top patterns})
371 across all players and games from the database\footnote{We use $n=500$ in our analysis.}.
372 For each player, we then count how many times was each of those $n$ patterns played
373 during all his games and finally assign him a~{\em pattern vector} $\vec p$ of dimension $n$, with each
374 dimension corresponding to the relative number of occurences of a given pattern
375 (with respect to player's most played \emph{top pattern}). Using relative numbers of occurences ensures that
376 each dimension of player's \emph{pattern vector} is scaled to range $[0,1]$ and
377 therefore even players with different number of games in the database have comparable \emph{pattern vectors}.
379 \subsection{Pattern Features}
380 We need to define how to compose the patterns we use to describe moves.
381 There are some tradeoffs in play - overly general descriptions carry too few
382 information to discern various player attributes; too specific descriptions
383 gather too few specimen over the games sample and the vector differences are
384 not statistically significant.
386 We have chosen an intuitive and simple approach inspired by pattern features
387 used when computing ELO ratings for candidate patterns in Computer Go play.
388 \cite{ELO} Each pattern is a~combination of several {\em pattern features}
389 (name--value pairs) matched at the position of the played move.
390 We use these features:
392 \begin{itemize}
393 \item capture move flag
394 \item atari move flag
395 \item atari escape flag
396 \item contiguity-to-last flag --- whether the move has been played in one of 8 neighbors of the last move
397 \item contiguity-to-second-last flag
398 \item board edge distance --- only up to distance 4
399 \item spatial pattern --- configuration of stones around the played move
400 \end{itemize}
402 The spatial patterns are normalized (using a dictionary) to be always
403 black-to-play and maintain translational and rotational symmetry.
404 Configurations of radius between 2 and 9 in the gridcular metric%
405 \footnote{The {\em gridcular} metric
406 $d(x,y) = |\delta x| + |\delta y| + \max(|\delta x|, |\delta y|)$ defines
407 a circle-like structure on the Go board square grid. \cite{SpatPat} }
408 are matched.
410 \subsection{Implementation}
412 We have implemented the data extraction by making use of the pattern
413 features matching implementation within the Pachi go-playing program
414 (TODO). We extract information on players by converting the SGF game
415 records to GTP (TODO) stream that feeds Pachi's {\tt patternscan}
416 engine which outputs a~single {\em patternspec} (string representation
417 of the particular pattern features combination) per move.
419 We can then gather all patternspecs played by a~given player and summarize
420 them; the $\vec p$ vector then consists of normalized counts of
421 the given $n$ most frequent patternspecs.
424 \section{Data Mining}
425 \label{data-mining}
427 To assess the properties of gathered \emph{pattern vectors}
428 and their influence on playing styles,
429 we have processes the data using a~few basic data minining techniques.
431 The first two methods ({\em analytic}) rely purely on data gathered
432 from the game collection
433 and serve to show internal structure and correlations within the data set.
434 Principal component analysis finds orthogonal vector components that
435 have the largest variance.
436 Reversing the process then indicates which patterns correlate with each style.
437 Additionally, PCA can be used as a vector-preprocessing for methods
438 that are negatively sensitive to \emph{pattern vector} component correlations.
440 A~second method -- Kohonen maps -- is based on the theory of self-organizing maps of abstract neurons that
441 compete against each other for representation of the input space.
442 Because neurons in the network are organized in a two-dimensional plane,
443 the trained network virtually spreads vectors to the 2D plane,
444 allowing for simple visualization of clusters of players with similar styles.
446 TODO: style vector -> output vector?
448 Furthermore, we have used and compared two \emph{classification} methods
449 that approximate well-defined but unknown \emph{style vector} $\vec S$
450 based on input \emph{pattern vector} $\vec P$.
451 The methods are calibrated based on expert or prior knowledge about
452 training pattern vectors and then their error is measured on a testing
453 set of pattern vectors.
455 One of the methods is $k$-Nearest Neighbor (kNN) classifier:
456 we approximate $\vec S$ by composing the \emph{style vectors} of $k$ nearest \emph{pattern vectors}.
457 The other is based on a multi-layer feed-forward Artificial Neural Network:
458 the neural network can learn correlations between input and output vectors
459 and generalize the ``knowledge'' to unknown vectors; it can be more flexible
460 in the interpretation of different pattern vector elements and discern more
461 complex relations than the kNN classifier, but e.g. requires larger training sample.
463 TODO: Dava ta posledni veta nejaky smysl?!
465 \subsection{Principal Component Analysis}
466 \label{data-mining}
467 We use Principal Component Analysis \emph{PCA} \cite{Jolliffe1986}
468 to reduce the dimensions of the \emph{pattern vectors} while preserving
469 as much information as possible.
471 Briefly, PCA is an eigenvalue decomposition of a~covariance matrix of centered \emph{pattern vectors},
472 producing a~linear mapping $o$ from $n$-dimensional vector space
473 to a~reduced $m$-dimensional vector space.
474 The $m$ eigenvectors of the original vectors' covariance matrix
475 with the largest eigenvalues are used as the base of the reduced vector space;
476 the eigenvectors form the transformation matrix $W$.
478 For each original \emph{pattern vector} $\vec p_i$,
479 we obtain its new representation $\vec r_i$ in the PCA base
480 as shown in the following equation:
481 \begin{equation}
482 \vec r_i = W \cdot \vec p_i
483 \end{equation}
485 The whole process is described in the Algorithm \ref{alg:pca}.
487 \begin{algorithm}
488 \caption{PCA -- Principal Component Analysis}
489 \begin{algorithmic}
490 \label{alg:pca}
491 \REQUIRE{$m > 0$, set of players $R$ with \emph{pattern vectors} $p_r$}
492 \STATE $\vec \mu \leftarrow 1/|R| \cdot \sum_{r \in R}{\vec p_r}$
493 \FOR{ $r \in R$}
494 \STATE $\vec p_r \leftarrow \vec p_r - \vec \mu$
496 \FOR{ $(i,j) \in \{1,... ,n\} \times \{1,... ,n\}$}
497 \STATE $\mathit{Cov}[i,j] \leftarrow 1/|R| \cdot \sum_{r \in R}{\vec p_{ri} \cdot \vec p_{rj}}$
499 \STATE Compute Eigenvalue Decomposition of $\mathit{Cov}$ matrix
500 \STATE Get $m$ largest eigenvalues
501 \STATE Most significant eigenvectors ordered by decreasing eigenvalues form the rows of matrix $W$
502 \FOR{ $r \in R$}
503 \STATE $\vec r_r\leftarrow W \vec p_r$
505 \end{algorithmic}
506 \end{algorithm}
508 \subsection{Kohonen Maps}
509 \label{koh}
510 Kohonen map is a self-organizing network with neurons spread over a two-dimensional plane.
511 Neurons in the map compete for representation of portions of the input vector space.
512 Each neuron $\vec n$ represents a vector
513 and the network is trained so that the neurons that are topologically close
514 tend to represent vectors that are close as well.
516 First, a randomly initialized network is sequentially trained;
517 in each iteration, we choose a random training vector $\vec t$
518 and find the neuron $\vec w$ that is closest to $\vec t$ in Euclidean metric
519 (we call $\vec w$ a \emph{winner neuron}).
521 We then adapt neurons from the neighbourhood of $\vec w$ employing an equation:
522 \begin{equation}
523 \vec n = \vec n + \alpha \cdot \mathit{Influence}(\vec w, \vec n) \cdot (\vec t - \vec n)
524 \end{equation}
525 where $\alpha$ is a learning parameter, usually decreasing in time.
526 $Influence()$ is a function that forces neurons to spread.
527 Such function is usually realised using a mexican hat function or a difference-of-gaussians
528 (see \cite{TODO} for details).
529 The state of the network can be evaluated by calculating mean square difference
530 between each $\vec t \in T$ and its corresponding \emph{winner neuron} $\vec w_t$:
531 \begin{equation}
532 \mathit{Error}(N,T) = \sum_{\vec t \in T}{|\vec w_t - \vec t|}
533 \end{equation}
536 \begin{algorithm}
537 \caption{Kohonen maps -- training}
538 \begin{algorithmic}
539 \label{alg:koh}
540 \REQUIRE{Set of training vectors $T$, input dimension $D$}
541 \REQUIRE{max number of iterations $M$, desired error $E$}
542 \STATE $N \leftarrow \{\vec n | \vec n$ random, $\mathit{dim}(\vec n) = D\}$
544 \STATE $\mathit{It} \leftarrow \mathit{It} + 1$
545 \STATE $\vec t \leftarrow \mathit{PickRandom}(T)$
546 \FORALL{$\vec n \in N$}
547 \STATE $D[\vec n] \leftarrow \mathit{EuclideanDistance}(\vec n, \vec t)$
549 \STATE Find $ \vec w \in N$ so that $D[\vec w] <= D[\vec m], \forall \vec m \in N$
550 \FORALL{$\vec n \in \mathit{TopologicalNeigbors}(N, \vec w)$}
551 \STATE $\vec n \leftarrow \vec n + \alpha(It) \cdot \mathit{Influence}(\vec w, \vec n) \cdot ( \vec t - \vec n ) $
553 \UNTIL{$\mathit{Error}(N, T) < E$ or $ \mathit{It} > M$}
554 \end{algorithmic}
555 \end{algorithm}
558 \subsection{k-nearest Neighbors Classifier}
559 \label{knn}
560 Our goal is to approximate player's \emph{style vector} $\vec S$
561 based on their \emph{pattern vector} $\vec P$.
562 To achieve this, we require prior knowledge of \emph{reference style vectors}
563 (see section \ref{style-vectors}).
565 In this method, we assume that similarities in players' \emph{pattern vectors}
566 uniformly correlate with similarities in players' \emph{style vectors}.
567 We try to approximate $\vec S$ as a weighted average of \emph{style vectors}
568 $\vec s_i$ of $k$ players with \emph{pattern vectors} $\vec p_i$ closest to $\vec P$.
569 This is illustrated in the Algorithm \ref{alg:knn}.
570 Note that the weight is a function of distance and it is not explicitly defined in Algorithm \ref{alg:knn}.
571 During our research, exponentially decreasing weight has proven to be sufficient.
573 \begin{algorithm}
574 \caption{k-Nearest Neighbors}
575 \begin{algorithmic}
576 \label{alg:knn}
577 \REQUIRE{pattern vector $\vec P$, $k > 0$, set of reference players $R$}
578 \FORALL{$r \in R$ }
579 \STATE $D[r] \leftarrow \mathit{EuclideanDistance}(\vec p_r, \vec P)$
581 \STATE $N \leftarrow \mathit{SelectSmallest}(k, R, D)$
582 \STATE $\vec S \leftarrow \vec 0$
583 \FORALL{$r \in N $}
584 \STATE $\vec S \leftarrow \vec S + \mathit{Weight}(D[r]) \cdot \vec s_r $
586 \end{algorithmic}
587 \end{algorithm}
589 \subsection{Neural Network Classifier}
590 \label{neural-net}
592 As an alternative to the k-Nearest Neigbors algorithm (section \ref{knn}),
593 we have used a classificator based on feed-forward artificial neural networks \cite{TODO}.
594 Neural networks (NN) are known for their ability to generalize
595 and find correlations and patterns between input and output data.
596 Neural network is an adaptive system that must undergo a training
597 period before it can be reasonably used, similarly to the requirement
598 of reference vectors for the k-Nearest Neighbors algorithm above.
600 \subsubsection{Computation and activation of the NN}
601 Technically, neural network is a network of interconnected computational units called neurons.
602 A feedforward neural network has a layered topology;
603 it usually has one \emph{input layer}, one \emph{output layer}
604 and an arbitrary number of \emph{hidden layers} inbetween.
606 Each neuron $i$ is connected to all neurons in the previous layer and each connection has its weight $w_{ij}$
608 The computation proceeds in discrete time steps.
609 In the first step, the neurons in the \emph{input layer}
610 are \emph{activated} according to the \emph{input vector}.
611 Then, we iteratively compute output of each neuron in the next layer
612 until the output layer is reached.
613 The activity of output layer is then presented as the result.
615 The activation $y_i$ of neuron $i$ from the layer $I$ is computed as
616 \begin{equation}
617 y_i = f(\sum_{j \in J}{w_{ij} y_j})
618 \end{equation}
619 where $J$ is the previous layer, while $y_j$ is the activation for neurons from $J$ layer.
620 Function $f()$ is so-called \emph{activation function}
621 and its purpose is to bound the outputs of neurons.
622 A typical example of an activation function is the sigmoid function.%
623 \footnote{A special case of the logistic function, defined by the formula
624 $\sigma(x)=\frac{1}{1+e^{-(rx+k)}}$; parameters control the growth rate ($r$)
625 and the x-position ($k$).}
627 \subsubsection{Training}
628 The training of the feed-forward neural network usually involves some
629 modification of supervised Backpropagation learning algorithm. \cite{TODO}
630 We use first-order optimization algorithm called RPROP \cite{Riedmiller1993}.
632 Because the \emph{reference set} is usually not very large,
633 we have devised a simple method for its extension.
634 This enhancement is based upon adding random linear combinations
635 of \emph{style and pattern vectors} to the training set.
637 TODO: Tohle je puvodni napad?
639 As outlined above, the training set consists of pairs of
640 input vectors (\emph{pattern vectors}) and
641 desired output vectors (\emph{style vectors}).
642 The training set $T$ is then extended by adding the linear combinations:
643 \begin{equation}
644 T_\mathit{base} = \{(\vec p_r, \vec s_r) | r \in R\}\\
645 \end{equation}
646 \begin{equation}
647 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}\}
648 \end{equation}
649 TODO zabudovat $g_d$ dovnitr?
650 where $g_d, d \in D$ are random coeficients, so that $\sum_{d \in D}{g_d} = 1$.
651 The training set is then constructed as:
652 \begin{equation}
653 T = T_\mathit{base} \cup \mathit{SomeFiniteSubset}(T_\mathit{ext})
654 \end{equation}
656 The network is trained as shown in Algorithm \ref{alg:tnn}.
658 \begin{algorithm}
659 \caption{Training Neural Network}
660 \begin{algorithmic}
661 \label{alg:tnn}
662 \REQUIRE{Train set $T$, desired error $e$, max iterations $M$}
663 \STATE $N \leftarrow \mathit{RandomlyInitializedNetwork}()$
664 \STATE $\mathit{It} \leftarrow 0$
666 \STATE $\mathit{It} \leftarrow \mathit{It} + 1$
667 \STATE $\Delta \vec w \leftarrow \vec 0$
668 \STATE $\mathit{TotalError} \leftarrow 0$
669 %\FORALL{$(\overrightarrow{Input}, \overrightarrow{DesiredOutput}) \in T$}
670 %\STATE $\overrightarrow{Output} \leftarrow Result(N, \overrightarrow{Input})$
671 %\STATE $E \leftarrow |\overrightarrow{DesiredOutput} - \overrightarrow{Output}|$
672 \FORALL{$(\mathit{Input}, \mathit{DesiredOutput}) \in T$}
673 \STATE $\mathit{Output} \leftarrow \mathit{Result}(N, \mathit{Input})$
674 \STATE $\mathit{Error} \leftarrow |\mathit{DesiredOutput} - \mathit{Output}|$
675 \STATE $\Delta \vec w \leftarrow \Delta \vec w + \mathit{WeightUpdate}(N,\mathit{Error})$
676 \STATE $\mathit{TotalError} \leftarrow \mathit{TotalError} + \mathit{Error}$
678 \STATE $N \leftarrow \mathit{ModifyWeights}(N, \Delta \vec w)$
679 \UNTIL{$\mathit{TotalError} < e$ or $ \mathit{It} > M$}
680 \end{algorithmic}
681 \end{algorithm}
684 \subsubsection{Architecture details}
685 TODO num layers, num neurons, ..
688 \subsection{Implementation}
690 We have implemented the data mining methods as an open-source framework ``gostyle'' \cite{TODO},
691 made available under the GNU GPL licence.
692 We use python for the basic processing and most of the analysis;
693 the MDP library \cite{MDP} is used for PCA analysis, Kohonen library \cite{KohonenPy} for Kohonen maps.
694 The neuron network classifier is using the libfann C library. \cite{TODO}
697 \section{Strength Estimator}
699 First, we have used our framework to analyse correlations of pattern vectors
700 and playing strength. Like in other competitively played board games, Go players
701 receive real-world rating based on tournament games, and rank based on their
702 rating.\footnote{Elo-like rating system \cite{GoR} is usually used,
703 corresponding to even win chances for game of two players with the same rank,
704 and about 2:3 win chance for white in case of one rank difference.}%
705 \footnote{Professional ranks and dan ranks in some Asia countries may
706 be assigned differently.} The amateur ranks range from 30kyu (beginner) to
707 1kyu (intermediate) and then follows 1dan to 7dan (9dan in some systems;
708 top-level player). Multiple independent real-world ranking scales exist
709 (geographically based) and online servers maintain their own user ranking;
710 the difference can be up to several stones.
712 As the source game collection, we use Go Teaching Ladder
713 reviews\footnote{The reviews contain comments and variations --- we consider only the actual played game.}
714 \cite{GTL} --- this collection contains 7700 games of players with strength ranging
715 from 30k to 4d; we consider only even games with clear rank information, and then
716 randomly separate 770 games as a testing set. Since the rank information is provided
717 by the users and may not be consistent, we are forced to take a simplified look
718 at the ranks, discarding the differences between various systems and thus increasing
719 error in our model.\footnote{Since
720 our results seem satisfying, we did not pursue to try another collection}
722 First, we have created a single pattern vector for each rank, from 30k to 4d;
723 we have performed PCA analysis on the pattern vectors, achieving near-perfect
724 rank correspondence in the first PCA dimension\footnote{The eigenvalue of the
725 second dimension was four orders of magnitude smaller, with no discernable
726 structure revealed within the lower-order eigenvectors.}
727 (chi-square test TODO).
728 (Figure TODO.) Using the eigenvector position directly for classification
729 of players within the test group yields MSE TODO, thus providing
730 reasonably satisfying accuracy.
732 To further enhance the strength estimator accuracy,
733 we have tried to train a NN classifier on our train set, consisting
734 of one $(\vec p, {\rm rank})$ pair per player --- we use the pattern vector
735 for activation of input neurons and rank number as result of the output
736 neuron. We then proceeded to test the NN on per-player pattern vectors built
737 from the games in the test set, yielding MSE of TODO with TODO games per player
738 on average.
741 \section{Style Estimator}
743 The source games collection is GoGoD Winter 2009 (TODO) containing 42000 (TODO)
744 professional games, dating from the early Go history 1500 years ago to the present.
746 bla bla bla
748 \subsection{Expert-based knowledge}
749 \label{style-vectors}
750 In order to provide a reference frame for our style analysis,
751 we have gathered some expert-based information about various
752 traditionally perceived style aspects.
753 Three high-level Go players (Alexander Dinerstein 3-pro, Motoki Noguchi
754 7-dan and Vit Brunner 4-dan) have judged style of several Go
755 professionals -- we call them \emph{reference playerse} -- chosen for both
756 being well-known within the community and having large number of played games in our collection.
758 This expert-based knowledge allows us to predict styles of unknown players based on
759 the similarity of their pattern vectors, as well as discover correlations between
760 styles and proportions of played patterns.
762 Experts were asked to assign each of player's style a number
763 on a scale from 1 to 10. These are interpreted
764 as shown in the table below.
766 \vspace{4mm}
767 \noindent
768 %\begin{table}
769 \begin{center}
770 %\caption{Styles}
771 \begin{tabular}{|c|c|c|}
772 \hline
773 \multicolumn{3}{|c|}{Styles} \\ \hline
774 Style & 1 & 10\\ \hline
775 Territoriality & Moyo & Territorial \\
776 Orthodoxity & Classic & Novel \\
777 Aggressivity & Calm & Figting \\
778 Thickness & Safe & Shinogi \\ \hline
779 \end{tabular}
780 \end{center}
781 %\end{table}
782 \vspace{4mm}
784 Averaging this expert based evaluation yields
785 \emph{reference style vector} $\vec s_r$ (of dimension $4$) for each player $r$
786 from the set of \emph{reference players} $R$.
788 \subsection{Style Components Analysis}
790 PCA analysis yielded X, chi-square test...
792 \subsection{Style Classification}
794 We then tried to apply the NN classifier with linear output function on the dataset
795 and that yielded Y (see fig. Z), with MSE abcd.
798 \section{Proposed Applications}
800 We believe that our findings might be useful for many applications
801 in the area of Go support software as well as Go-playing computer engines.
803 The style analysis can be an excellent teaching aid --- classifying style
804 dimensions based on player's pattern vector, many study recommendations
805 can be given, e.g. about the professional games to replay, the goal being
806 balancing understanding of various styles to achieve well-rounded skill set.
807 This was also our original aim when starting the research and a user-friendly
808 tool based on our work is now being created.
810 We hope that more strong players will look into the style dimensions found
811 by our statistical analysis --- analysis of most played patterns of prospective
812 opponents might prepare for the game, but we especially hope that new insights
813 on strategic purposes of various shapes and general human understanding
814 of the game might be achieved by investigating the style-specific patterns.
816 Classifying playing strength of a pattern vector of a player can be used
817 e.g. to help determine initial real-world rating of a player before their
818 first tournament based on games played on the internet; some players especially
819 in less populated areas could get fairly strong before playing their first
820 real tournament.
822 Analysis of pattern vectors extracted from games of Go-playing programs
823 in light of the shown strength and style distributions might help to
824 highlight some weaknesses and room for improvements. (However, since
825 correlation does not imply causation, simply optimizing Go-playing programs
826 according to these vectors is unlikely to yield good results.)
827 Another interesting applications in Go-playing programs might be strength
828 adjustment; the program can classify the player's level based on the pattern
829 vector from its previous games and auto-adjust its difficulty settings
830 accordingly to provide more even games for beginners.
833 % An example of a floating figure using the graphicx package.
834 % Note that \label must occur AFTER (or within) \caption.
835 % For figures, \caption should occur after the \includegraphics.
836 % Note that IEEEtran v1.7 and later has special internal code that
837 % is designed to preserve the operation of \label within \caption
838 % even when the captionsoff option is in effect. However, because
839 % of issues like this, it may be the safest practice to put all your
840 % \label just after \caption rather than within \caption{}.
842 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
843 % option should be used if it is desired that the figures are to be
844 % displayed while in draft mode.
846 %\begin{figure}[!t]
847 %\centering
848 %\includegraphics[width=2.5in]{myfigure}
849 % where an .eps filename suffix will be assumed under latex,
850 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
851 % via \DeclareGraphicsExtensions.
852 %\caption{Simulation Results}
853 %\label{fig_sim}
854 %\end{figure}
856 % Note that IEEE typically puts floats only at the top, even when this
857 % results in a large percentage of a column being occupied by floats.
860 % An example of a double column floating figure using two subfigures.
861 % (The subfig.sty package must be loaded for this to work.)
862 % The subfigure \label commands are set within each subfloat command, the
863 % \label for the overall figure must come after \caption.
864 % \hfil must be used as a separator to get equal spacing.
865 % The subfigure.sty package works much the same way, except \subfigure is
866 % used instead of \subfloat.
868 %\begin{figure*}[!t]
869 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
870 %\label{fig_first_case}}
871 %\hfil
872 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
873 %\label{fig_second_case}}}
874 %\caption{Simulation results}
875 %\label{fig_sim}
876 %\end{figure*}
878 % Note that often IEEE papers with subfigures do not employ subfigure
879 % captions (using the optional argument to \subfloat), but instead will
880 % reference/describe all of them (a), (b), etc., within the main caption.
883 % An example of a floating table. Note that, for IEEE style tables, the
884 % \caption command should come BEFORE the table. Table text will default to
885 % \footnotesize as IEEE normally uses this smaller font for tables.
886 % The \label must come after \caption as always.
888 %\begin{table}[!t]
889 %% increase table row spacing, adjust to taste
890 %\renewcommand{\arraystretch}{1.3}
891 % if using array.sty, it might be a good idea to tweak the value of
892 % \extrarowheight as needed to properly center the text within the cells
893 %\caption{An Example of a Table}
894 %\label{table_example}
895 %\centering
896 %% Some packages, such as MDW tools, offer better commands for making tables
897 %% than the plain LaTeX2e tabular which is used here.
898 %\begin{tabular}{|c||c|}
899 %\hline
900 %One & Two\\
901 %\hline
902 %Three & Four\\
903 %\hline
904 %\end{tabular}
905 %\end{table}
908 % Note that IEEE does not put floats in the very first column - or typically
909 % anywhere on the first page for that matter. Also, in-text middle ("here")
910 % positioning is not used. Most IEEE journals use top floats exclusively.
911 % Note that, LaTeX2e, unlike IEEE journals, places footnotes above bottom
912 % floats. This can be corrected via the \fnbelowfloat command of the
913 % stfloats package.
917 \section{Conclusion}
918 The conclusion goes here.
919 We have shown brm and proposed brm.
921 Since we are not aware of any previous research on this topic and we
922 are limited by space and time constraints, plenty of research remains
923 to be done. There is plenty of room for further research in all parts
924 of our analysis --- different methods of generating the $\vec p$ vectors
925 can be explored; other data mining methods could be tried.
926 It can be argued that many players adjust their style by game conditions
927 (Go development era, handicap, komi and color, time limits, opponent)
928 or styles might express differently in various game stages.
929 More professional players could be consulted on the findings
930 and for style scales calibration. Impact of handicap games on by-strength
931 $\vec p$ distribution should be investigated.
933 TODO: Future research --- Sparse PCA
938 % if have a single appendix:
939 %\appendix[Proof of the Zonklar Equations]
940 % or
941 %\appendix % for no appendix heading
942 % do not use \section anymore after \appendix, only \section*
943 % is possibly needed
945 % use appendices with more than one appendix
946 % then use \section to start each appendix
947 % you must declare a \section before using any
948 % \subsection or using \label (\appendices by itself
949 % starts a section numbered zero.)
953 %\appendices
954 %\section{Proof of the First Zonklar Equation}
955 %Appendix one text goes here.
957 %% you can choose not to have a title for an appendix
958 %% if you want by leaving the argument blank
959 %\section{}
960 %Appendix two text goes here.
963 % use section* for acknowledgement
964 \section*{Acknowledgment}
965 \label{acknowledgement}
968 We would like to thank X for reviewing our paper.
969 We appreciate helpful comments on our general methodology
970 by John Fairbairn, T. M. Hall, Robert Jasiek
971 and several GoDiscussions.com users. \cite{GoDiscThread}
972 Finally, we are very grateful for ranking of go styles of selected professionals
973 by Alexander Dinerstein 3-pro, Motoki Noguchi 7-dan and Vit Brunner 4-dan.
976 % Can use something like this to put references on a page
977 % by themselves when using endfloat and the captionsoff option.
978 \ifCLASSOPTIONcaptionsoff
979 \newpage
984 % trigger a \newpage just before the given reference
985 % number - used to balance the columns on the last page
986 % adjust value as needed - may need to be readjusted if
987 % the document is modified later
988 %\IEEEtriggeratref{8}
989 % The "triggered" command can be changed if desired:
990 %\IEEEtriggercmd{\enlargethispage{-5in}}
992 % references section
994 % can use a bibliography generated by BibTeX as a .bbl file
995 % BibTeX documentation can be easily obtained at:
996 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
997 % The IEEEtran BibTeX style support page is at:
998 % http://www.michaelshell.org/tex/ieeetran/bibtex/
999 \bibliographystyle{IEEEtran}
1000 % argument is your BibTeX string definitions and bibliography database(s)
1001 \bibliography{gostyle}
1003 % <OR> manually copy in the resultant .bbl file
1004 % set second argument of \begin to the number of references
1005 % (used to reserve space for the reference number labels box)
1006 %\begin{thebibliography}{1}
1008 %\bibitem{MasterMCTS}
1010 %\end{thebibliography}
1012 % biography section
1014 % If you have an EPS/PDF photo (graphicx package needed) extra braces are
1015 % needed around the contents of the optional argument to biography to prevent
1016 % the LaTeX parser from getting confused when it sees the complicated
1017 % \includegraphics command within an optional argument. (You could create
1018 % your own custom macro containing the \includegraphics command to make things
1019 % simpler here.)
1020 %\begin{biography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
1021 % or if you just want to reserve a space for a photo:
1023 \begin{IEEEbiography}{Michael Shell}
1024 Biography text here.
1025 \end{IEEEbiography}
1027 % if you will not have a photo at all:
1028 \begin{IEEEbiographynophoto}{John Doe}
1029 Biography text here.
1030 \end{IEEEbiographynophoto}
1032 % insert where needed to balance the two columns on the last page with
1033 % biographies
1034 %\newpage
1036 \begin{IEEEbiographynophoto}{Jane Doe}
1037 Biography text here.
1038 \end{IEEEbiographynophoto}
1040 % You can push biographies down or up by placing
1041 % a \vfill before or after them. The appropriate
1042 % use of \vfill depends on what kind of text is
1043 % on the last page and whether or not the columns
1044 % are being equalized.
1046 %\vfill
1048 % Can be used to pull up biographies so that the bottom of the last one
1049 % is flush with the other column.
1050 %\enlargethispage{-5in}
1054 % that's all folks
1055 \end{document}