tex: Data Mining cleanups all over the map
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209 \hyphenation{op-tical net-works semi-conduc-tor know-ledge}
212 \begin{document}
214 % paper title
215 % can use linebreaks \\ within to get better formatting as desired
216 \title{On Move Pattern Trends\\in Large Go Games Corpus}
218 % use \thanks{} to gain access to the first footnote area
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221 \author{Petr~Baudi\v{s},~Josef~Moud\v{r}\'{i}k% <-this % stops a space
222 \thanks{P. Baudi\v{s} 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
223 \thanks{J. Moud\v{r}\'{i}k is student at the Faculty of Math and Physics, Charles University, Prague, CZ.}}
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245 \markboth{Transactions on Computational Intelligence and AI in Games}%
246 {On Pattern Feature Trends in Large Go Game Corpus}
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272 % make the title area
273 \maketitle
276 \begin{abstract}
277 %\boldmath
279 We process a~large corpus of game records of the board game of Go and
280 propose a~way to extract summary information on played moves.
281 We then apply several basic data-mining methods on the summary
282 information to identify the most differentiating features within the
283 summary information, and discuss their correspondence with traditional
284 Go knowledge. We show mappings of the features to player attributes
285 like playing strength or informally perceived ``playing style'' (such as
286 territoriality or aggressivity), and propose applications including
287 seeding real-work ranks of internet players, aiding in Go study, or
288 contribution to Go-theoretical discussion on the scope of ``playing
289 style''.
291 \end{abstract}
292 % IEEEtran.cls defaults to using nonbold math in the Abstract.
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299 % Note that keywords are not normally used for peerreview papers.
300 \begin{IEEEkeywords}
301 board games, go, data mining, pattern recongition, player strength, playing style,
302 neural networks, Kohonen maps, principal component analysis
303 \end{IEEEkeywords}
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322 \section{Introduction}
323 % The very first letter is a 2 line initial drop letter followed
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337 % and "HIS" in caps to complete the first word.
338 \IEEEPARstart{T}{he} field of Computer Go usually focuses on the problem
339 of creating a~program to play the game, finding the best move from a~given
340 board position. \cite{GellySilver2008}
341 We will make use of one method developed in the course
342 of such research and apply it to the analysis of existing game records
343 with the aim of helping humans to play and understand the game better
344 instead.
346 Go is a~two-player full-information board game played
347 on a~square grid (usually $19\times19$ lines) with black and white
348 stones; the goal of the game is to surround the most territory and
349 capture enemy stones. We assume basic familiarity with the game.
351 Many Go players are eager to play using computers (usually over
352 the internet) and review games played by others on computers as well.
353 This means that large amounts of game records are collected and digitally
354 stored, enabling easy processing of such collections. However, so far
355 only little has been done with the available data --- we are aware
356 only of uses for simple win/loss statistics \cite{KGSStats} \cite{KGSAnalytics} \cite{ProGoR}
357 and ``next move'' statistics on a~specific position \cite{Kombilo} \cite{MoyoGo}.
359 We present a~more in-depth approach --- from all played moves, we devise
360 a~compact evaluation of each player. We then explore correlations between
361 evaluations of various players in light of externally given information.
362 This way, we can discover similarity between moves characteristics of
363 players with the same playing strength, or discuss the meaning of the
364 "playing style" concept on the assumption that similar playing styles
365 should yield similar moves characteristics.
368 \section{Data Extraction}
369 \label{pattern-vectors}
371 As the input of our analysis, we use large collections of game records%
372 \footnote{We use the SGF format \cite{SGF} in our implementation.}
373 grouped by the primary object of analysis (player name, player rank, etc.).
374 We process the games by object, generating a description for each
375 played move -- a {\em pattern}, being a combination of several
376 {\em pattern features} described below.
378 We keep track of the most
379 occuring patterns, finally composing $n$-dimensional {\em pattern vector}
380 $\vec p$ of per-pattern counts from the $n$ globally most frequent patterns%
381 \footnote{We use $n=500$ in our analysis.}
382 (the mapping from patterns to vector elements is common for all objects).
383 We can then process and compare just the pattern vectors.
385 The pattern vector elements can have diverse values since for each object,
386 we consider different number of games (and thus patterns).
387 Therefore, we linearly rescale and normalize the values to range $[-1,1]$,
388 the most frequent pattern having the value of $1$ and the least occuring
389 one being $-1$.%
390 \footnote{We did not investigate different methods of re-scaling the vectors;
391 that might be a good way of improving accuracy of our analysis.}
392 Thus, we obtain vectors describing relative frequency of played patterns
393 independent on number of gathered patterns.
395 \subsection{Pattern Features}
396 When deciding how to compose the patterns we use to describe moves,
397 we need to consider a specificity tradeoff --- overly general descriptions carry too few
398 information to discern various player attributes; too specific descriptions
399 gather too few specimen over the games sample and the vector differences are
400 not statistically significant.
402 We have chosen an intuitive and simple approach inspired by pattern features
403 used when computing Elo ratings for candidate patterns in Computer Go play.
404 \cite{Elo} Each pattern is a~combination of several {\em pattern features}
405 (name--value pairs) matched at the position of the played move.
406 We use these features:
408 \begin{itemize}
409 \item capture move flag
410 \item atari move flag
411 \item atari escape flag
412 \item contiguity-to-last flag --- whether the move has been played in one of 8 neighbors of the last move
413 \item contiguity-to-second-last flag
414 \item board edge distance --- only up to distance 4
415 \item spatial pattern --- configuration of stones around the played move
416 \end{itemize}
418 The spatial patterns are normalized (using a dictionary) to be always
419 black-to-play and maintain translational and rotational symmetry.
420 Configurations of radius between 2 and 9 in the gridcular metric%
421 \footnote{The {\em gridcular} metric
422 $d(x,y) = |\delta x| + |\delta y| + \max(|\delta x|, |\delta y|)$ defines
423 a circle-like structure on the Go board square grid. \cite{SpatPat} }
424 are matched.
426 Pattern vectors representing these features contain information on
427 played shape as well as basic representation of tactical dynamics
428 --- threats to capture stones, replying to last move, or ignoring
429 opponent's move elsewhere to return to an urgent local situation.
430 The shapes most frequently correspond to opening moves
431 (either in empty corners and sides, or as part of {\em joseki}
432 --- commonly played sequences) characteristic for a certain
433 strategic aim. In the opening, even a single-line difference
434 in the distance from the border can have dramatic impact on
435 further local and global development.
437 \subsection{Implementation}
439 We have implemented the data extraction by making use of the pattern
440 features matching implementation%
441 \footnote{The pattern features matching was developed according
442 to the Elo-rating playing scheme. \cite{Elo}}
443 within the Pachi go-playing program \cite{Pachi}.
444 We extract information on players by converting the SGF game
445 records to GTP stream \cite{GTP} that feeds Pachi's {\tt patternscan}
446 engine, outputting a~single {\em patternspec} (string representation
447 of the particular pattern features combination) per move. Of course,
448 only moves played by the appropriate color in the game are collected.
450 \section{Data Mining}
451 \label{data-mining}
453 To assess the properties of gathered pattern vectors
454 and their influence on playing styles,
455 we process the data by several basic data minining techniques.
457 The first two methods {\em (analytic)} rely purely on data gathered
458 from the game collection
459 and serve to show internal structure and correlations within the data set.
461 Principal Component Analysis finds orthogonal vector components that
462 have the largest variance.
463 Reversing the process can indicate which patterns correlate with each component.
464 Additionally, PCA can be used as vector preprocessing for methods
465 that are negatively sensitive to pattern vector component correlations.
467 The~second method of Kohonen Maps
468 is based on the theory of self-organizing maps of abstract units (neurons) that
469 compete against each other for the representation of the input space.
470 Because neurons in the network are organized in a two-dimensional plane,
471 the trained network spreads the vectors on a 2D plane,
472 allowing for visualization of clusters of players with similar properties.
475 Furthermore, we use two \emph{classification} methods that assign
476 each pattern vector $\vec P$ an \emph{output vector $\vec O$,
477 representing e.g.~information about styles, player's strength or even
478 meta-information like the player's era or a country of origin.
479 Initially, the methods must be calibrated (trained) on some prior knowledge,
480 usually in the form of \emph{reference pairs} of pattern vectors
481 and the associated output vectors.
483 Moreover, the reference set can be divided into training and testing pairs
484 and the methods can be compared by the mean square error on testing data set
485 (difference of output vectors approximated by the method and their real desired value).
487 %\footnote{However, note that dicrete characteristics such as country of origin are
488 %not very feasible to use here, since WHAT??? is that even true?? }
490 The $k$-Nearest Neighbors \cite{CoverHart1967} classifier
491 approximates $\vec O$ by composing the output vectors
492 of $k$ reference pattern vectors closest to $\vec P$.
494 The other classifier is a~multi-layer feed-forward Artificial Neural Network:
495 the neural network can learn correlations between input and output vectors
496 and generalize the ``knowledge'' to unknown vectors; it can be more flexible
497 in the interpretation of different pattern vector elements and discern more
498 complex relations than the kNN classifier,
499 but may not be as stable and requires larger training sample.
501 \subsection{Principal Component Analysis}
502 \label{data-mining}
503 We use Principal Component Analysis \emph{PCA} \cite{Jolliffe1986}
504 to reduce the dimensions of the pattern vectors while preserving
505 as much information as possible, assuming inter-dependencies between
506 pattern vector dimensions are linear.
508 Briefly, PCA is an eigenvalue decomposition of a~covariance matrix of centered pattern vectors,
509 producing a~linear mapping $o$ from $n$-dimensional vector space
510 to a~reduced $m$-dimensional vector space.
511 The $m$ eigenvectors of the original vectors' covariance matrix
512 with the largest eigenvalues are used as the base of the reduced vector space;
513 the eigenvectors form projection matrix $W$.
515 For each original pattern vector $\vec p_i$,
516 we obtain its new representation $\vec r_i$ in the PCA base
517 as shown in the following equation:
518 \begin{equation}
519 \vec r_i = W \cdot \vec p_i
520 \end{equation}
522 The whole process is described in the Algorithm \ref{alg:pca}.
524 \begin{algorithm}
525 \caption{PCA -- Principal Component Analysis}
526 \begin{algorithmic}
527 \label{alg:pca}
528 \REQUIRE{$m > 0$, set of players $R$ with pattern vectors $p_r$}
529 \STATE $\vec \mu \leftarrow 1/|R| \cdot \sum_{r \in R}{\vec p_r}$
530 \FOR{ $r \in R$}
531 \STATE $\vec p_r \leftarrow \vec p_r - \vec \mu$
532 \ENDFOR
533 \FOR{ $(i,j) \in \{1,... ,n\} \times \{1,... ,n\}$}
534 \STATE $\mathit{Cov}[i,j] \leftarrow 1/|R| \cdot \sum_{r \in R}{\vec p_{ri} \cdot \vec p_{rj}}$
535 \ENDFOR
536 \STATE Compute Eigenvalue Decomposition of $\mathit{Cov}$ matrix
537 \STATE Get $m$ largest eigenvalues
538 \STATE Most significant eigenvectors ordered by decreasing eigenvalues form the rows of matrix $W$
539 \FOR{ $r \in R$}
540 \STATE $\vec r_r\leftarrow W \vec p_r$
541 \ENDFOR
542 \end{algorithmic}
543 \end{algorithm}
545 \label{pearson}
546 We want to find correlations between PCA dimensions and
547 some prior knowledge (player rank, style vector).
548 For this purpose, we compute the well-known
549 {\em Pearson product-moment correlation coefficient} \cite{Pearson},
550 measuring the strength of the linear dependence%
551 \footnote{A desirable property of PMCC is that it is invariant to translations and rescaling
552 of the vectors.}
553 between the dimensions:
555 $$ r_{X,Y} = {{\rm cov}(X,Y) \over \sigma_X \sigma_Y} $$
557 \subsection{Kohonen Maps}
558 \label{koh}
559 Kohonen map is a self-organizing network with neurons spread evenly over a~two-dimensional plane.
560 Neurons $\vec n$ in the map compete for representation of portions of the input vector space,
561 each vector being represented by some neuron.
562 The network is trained so that the neurons
563 that are topologically close tend to represent vectors that are close in suitable metric as well.
565 First, a~randomly initialized network is sequentially trained;
566 in each iteration, we choose a~random training vector $\vec t$
567 and find the {\em winner neuron} $\vec w$ that is closest to $\vec t$ in Euclidean metric.
569 We then adapt neurons $n$ from the neighborhood of $\vec w$ employing the equation
570 \begin{equation}
571 \vec n = \vec n + \alpha \cdot \mathit{Influence}(\vec w, \vec n) \cdot (\vec t - \vec n)
572 \end{equation}
573 where $\alpha$ is a learning parameter, usually decreasing in time.
574 $Influence()$ is a function that forces neurons to spread.
575 Such function is usually realised using a mexican hat function or a difference-of-gaussians
576 \cite{TODO}.
577 The state of the network can be evaluated by calculating mean square difference
578 between each $\vec t \in T$ and its corresponding winner neuron $\vec w_t$:
579 \begin{equation}
580 \mathit{Error}(N,T) = \sum_{\vec t \in T}{|\vec w_t - \vec t|}
581 \end{equation}
584 \begin{algorithm}
585 \caption{Kohonen maps -- training}
586 \begin{algorithmic}
587 \label{alg:koh}
588 \REQUIRE{Set of training vectors $T$, input dimension $D$}
589 \REQUIRE{max number of iterations $M$, desired error $E$}
590 \STATE $N \leftarrow \{\vec n | \vec n$ random, $\mathit{dim}(\vec n) = D\}$
591 \REPEAT
592 \STATE $\mathit{It} \leftarrow \mathit{It} + 1$
593 \STATE $\vec t \leftarrow \mathit{PickRandom}(T)$
594 \FORALL{$\vec n \in N$}
595 \STATE $D[\vec n] \leftarrow \mathit{EuclideanDistance}(\vec n, \vec t)$
596 \ENDFOR
597 \STATE Find $ \vec w \in N$ so that $D[\vec w] <= D[\vec m], \forall \vec m \in N$
598 \FORALL{$\vec n \in \mathit{TopologicalNeigbors}(N, \vec w)$}
599 \STATE $\vec n \leftarrow \vec n + \alpha(It) \cdot \mathit{Influence}(\vec w, \vec n) \cdot ( \vec t - \vec n ) $
600 \ENDFOR
601 \UNTIL{$\mathit{Error}(N, T) < E$ or $ \mathit{It} > M$}
602 \end{algorithmic}
603 \end{algorithm}
606 \subsection{k-nearest Neighbors Classifier}
607 \label{knn}
608 Our goal is to approximate player's output vector $\vec O$;
609 we know his pattern vector $\vec P$.
610 We further assume that similarities in players' pattern vectors
611 uniformly correlate with similarities in players' output vectors.
613 We require a set of reference players $R$ with known \emph{pattern vectors} $\vec p_r$
614 and \emph{output vectors} $\vec o_r$.
616 $\vec O$ is approximated as a~weighted average of \emph{output vectors}
617 $\vec o_i$ of $k$ players with \emph{pattern vectors} $\vec p_i$ closest to $\vec P$.
618 This is illustrated in the Algorithm \ref{alg:knn}.
619 Note that the weight is a function of distance and is not explicitly defined in Algorithm \ref{alg:knn}.
620 During our research, exponentially decreasing weight has proven to be sufficient.
622 \begin{algorithm}
623 \caption{k-Nearest Neighbors}
624 \begin{algorithmic}
625 \label{alg:knn}
626 \REQUIRE{pattern vector $\vec P$, $k > 0$, set of reference players $R$}
627 \FORALL{$r \in R$ }
628 \STATE $D[r] \leftarrow \mathit{EuclideanDistance}(\vec p_r, \vec P)$
629 \ENDFOR
630 \STATE $N \leftarrow \mathit{SelectSmallest}(k, R, D)$
631 \STATE $\vec O \leftarrow \vec 0$
632 \FORALL{$r \in N $}
633 \STATE $\vec O \leftarrow \vec O + \mathit{Weight}(D[r]) \cdot \vec o_r $
634 \ENDFOR
635 \end{algorithmic}
636 \end{algorithm}
638 \subsection{Neural Network Classifier}
639 \label{neural-net}
641 Feed-forward neural networks \cite{ANN} are known for their ability to generalize
642 and find correlations between input patterns and output classifications.
643 Before use, the network is iteratively trained on the training data
644 until the error on the training set is reasonably small.
646 %Neural network is an adaptive system that must undergo a training
647 %period similarly to the requirement
648 %of reference vectors for the k-Nearest Neighbors algorithm above.
650 \subsubsection{Computation and activation of the NN}
651 Technically, the neural network is a network of interconnected
652 computational units called neurons.
653 A feedforward neural network has a layered topology;
654 it usually has one \emph{input layer}, one \emph{output layer}
655 and an arbitrary number of \emph{hidden layers} between.
657 Each neuron $i$ is connected to all neurons in the previous layer and each connection has its weight $w_{ij}$
659 The computation proceeds in discrete time steps.
660 In the first step, the neurons in the \emph{input layer}
661 are \emph{activated} according to the \emph{input vector}.
662 Then, we iteratively compute output of each neuron in the next layer
663 until the output layer is reached.
664 The activity of output layer is then presented as the result.
666 The activation $y_i$ of neuron $i$ from the layer $I$ is computed as
667 \begin{equation}
668 y_i = f\left(\sum_{j \in J}{w_{ij} y_j}\right)
669 \end{equation}
670 where $J$ is the previous layer, while $y_j$ is the activation for neurons from $J$ layer.
671 Function $f()$ is a~so-called \emph{activation function}
672 and its purpose is to bound the outputs of neurons.
673 A typical example of an activation function is the sigmoid function.%
674 \footnote{A special case of the logistic function, defined by the formula
675 $\sigma(x)=\frac{1}{1+e^{-(rx+k)}}$; parameters control the growth rate ($r$)
676 and the x-position ($k$).}
678 \subsubsection{Training}
679 Training of the feed-forward neural network usually involves some
680 modification of supervised Backpropagation learning algorithm.
681 We use first-order optimization algorithm called RPROP. \cite{Riedmiller1993}
683 %Because the \emph{reference set} is usually not very large,
684 %we have devised a simple method for its extension.
685 %This enhancement is based upon adding random linear combinations
686 %of \emph{style and pattern vectors} to the training set.
688 As outlined above, the training set $T$ consists of
689 $(\vec p_i, \vec o_i)$ pairs.
690 The training algorithm is shown in Algorithm \ref{alg:tnn}.
692 \begin{algorithm}
693 \caption{Training Neural Network}
694 \begin{algorithmic}
695 \label{alg:tnn}
696 \REQUIRE{Train set $T$, desired error $e$, max iterations $M$}
697 \STATE $N \leftarrow \mathit{RandomlyInitializedNetwork}()$
698 \STATE $\mathit{It} \leftarrow 0$
699 \REPEAT
700 \STATE $\mathit{It} \leftarrow \mathit{It} + 1$
701 \STATE $\Delta \vec w \leftarrow \vec 0$
702 \STATE $\mathit{TotalError} \leftarrow 0$
703 %\FORALL{$(\overrightarrow{Input}, \overrightarrow{DesiredOutput}) \in T$}
704 %\STATE $\overrightarrow{Output} \leftarrow Result(N, \overrightarrow{Input})$
705 %\STATE $E \leftarrow |\overrightarrow{DesiredOutput} - \overrightarrow{Output}|$
706 \FORALL{$(\mathit{Input}, \mathit{DesiredOutput}) \in T$}
707 \STATE $\mathit{Output} \leftarrow \mathit{Result}(N, \mathit{Input})$
708 \STATE $\mathit{Error} \leftarrow |\mathit{DesiredOutput} - \mathit{Output}|$
709 \STATE $\Delta \vec w \leftarrow \Delta \vec w + \mathit{WeightUpdate}(N,\mathit{Error})$
710 \STATE $\mathit{TotalError} \leftarrow \mathit{TotalError} + \mathit{Error}$
711 \ENDFOR
712 \STATE $N \leftarrow \mathit{ModifyWeights}(N, \Delta \vec w)$
713 \UNTIL{$\mathit{TotalError} < e$ or $ \mathit{It} > M$}
714 \end{algorithmic}
715 \end{algorithm}
717 \subsection{Implementation}
719 We have implemented the data mining methods as the
720 ``gostyle'' open-source framework \cite{GoStyle},
721 made available under the GNU GPL licence.
723 The majority of our basic processing and the analysis parts
724 are implemented in the Python \cite{Python2005} programming language.
725 We use several external libraries, most notably the MDP library \cite{MDP} (used for PCA analysis)
726 and Kohonen library \cite{KohonenPy}.
727 The neural network part of the project is written using the libfann C library\cite{Nissen2003}.
730 \section{Strength Estimator}
732 \begin{figure*}[!t]
733 \centering
734 \includegraphics[width=7in]{strength-pca}
735 \caption{PCA of by-strength vectors}
736 \label{fig:strength_pca}
737 \end{figure*}
739 First, we have used our framework to analyse correlations of pattern vectors
740 and playing strength. Like in other competitively played board games, Go players
741 receive real-world rating based on tournament games, and rank based on their
742 rating.\footnote{Elo-like rating system \cite{GoR} is usually used,
743 corresponding to even win chances for game of two players with the same rank,
744 and about 2:3 win chance for stronger in case of one rank difference.}%
745 \footnote{Professional ranks and dan ranks in some Asia countries may
746 be assigned differently.} The amateur ranks range from 30kyu (beginner) to
747 1kyu (intermediate) and then follows 1dan to 7dan (9dan in some systems;
748 top-level player). Multiple independent real-world ranking scales exist
749 (geographically based) and online servers maintain their own user ranking;
750 the difference can be up to several stones.
752 As the source game collection, we use Go Teaching Ladder
753 reviews\footnote{The reviews contain comments and variations --- we consider only the actual played game.}
754 \cite{GTL} --- this collection contains 7700 games of players with strength ranging
755 from 30k to 4d; we consider only even games with clear rank information, and then
756 randomly separate 770 games as a testing set. Since the rank information is provided
757 by the users and may not be consistent, we are forced to take a simplified look
758 at the ranks, discarding the differences between various systems and thus increasing
759 error in our model.\footnote{Since
760 our results seem satisfying, we did not pursue to try another collection;
761 one could e.g. look at game archives of some Go server.}
763 First, we have created a single pattern vector for each rank, from 30k to 4d;
764 we have performed PCA analysis on the pattern vectors, achieving near-perfect
765 rank correspondence in the first PCA dimension%
766 \footnote{The eigenvalue of the second dimension was four times smaller,
767 with no discernable structure revealed within the lower-order eigenvectors.}
768 (figure \ref{fig:strength_pca}).
770 We measure the accuracy of strength approximation by the first dimension
771 using Pearson's $r$ (see \ref{pearson}), yielding satisfying value $r=0.979$.
772 Using the eigenvector position directly for classification
773 of players within the test group yields MSE TODO, thus providing
774 reasonably satisfying accuracy.
776 To further enhance the strength estimator accuracy,
777 we have tried to train a NN classifier on our train set, consisting
778 of one $(\vec p, {\rm rank})$ pair per player --- we use the pattern vector
779 for activation of input neurons and rank number as result of the output
780 neuron. We then proceeded to test the NN on per-player pattern vectors built
781 from the games in the test set, yielding MSE of TODO with TODO games per player
782 on average.
785 \section{Style Estimator}
787 As a~second case study for our pattern analysis, we investigate pattern vectors $\vec p$
788 of various well-known players, their relationships and correlations to prior
789 knowledge to explore its correlaction with extracted patterns. We look for
790 relationships between pattern vectors and perceived ``playing style'' and
791 attempt to use our classifiers to transform pattern vector $\vec p$ to style vector $\vec s$.
793 The source game collection is GoGoD Winter 2008 \cite{GoGoD} containing 55000
794 professional games, dating from the early Go history 1500 years ago to the present.
795 We consider only games of a small subset of players (fig. \ref{fig:style_marks});
796 we have chosen these for being well-known within the players community,
797 having large number of played games in our collection and not playing too long
798 ago.\footnote{Over time, many commonly used sequences get altered, adopted and
799 dismissed; usual playing conditions can also differ significantly.}
801 \subsection{Expert-based knowledge}
802 \label{style-vectors}
803 In order to provide a reference frame for our style analysis,
804 we have gathered some expert-based information about various
805 traditionally perceived style aspects.
806 This expert-based knowledge allows us to predict styles of unknown players based on
807 the similarity of their pattern vectors, as well as discover correlations between
808 styles and proportions of played patterns.
810 Experts were asked to mark each style aspect of the given players
811 on the scale from 1 to 10. The style aspects are defined as shown:
813 %\vspace{4mm}
814 %\noindent
815 \begin{table}
816 \begin{center}
817 \caption{Styles}
818 \begin{tabular}{|c|c|c|}
819 \hline
820 Style & 1 & 10\\ \hline
821 Territoriality $\tau$ & Moyo & Territory \\
822 Orthodoxity $\omega$ & Classic & Novel \\
823 Aggressivity $\alpha$ & Calm & Figting \\
824 Thickness $\theta$ & Safe & Shinogi \\ \hline
825 \end{tabular}
826 \end{center}
827 \end{table}
828 %\vspace{4mm}
830 Averaging this expert based evaluation yields
831 \emph{reference style vector} $\vec s_r$ (of dimension $4$) for each player $r$
832 from the set of \emph{reference players} $R$.
834 \begin{table}[!t]
835 % increase table row spacing, adjust to taste
836 \renewcommand{\arraystretch}{1.3}
837 \caption{Covariance Measure of Prior Information Dimensions}
838 \label{fig:style_marks_r}
839 \centering
840 % Some packages, such as MDW tools, offer better commands for making tables
841 % than the plain LaTeX2e tabular which is used here.
842 \begin{tabular}{|r||r||r||r||r||r|}
843 \hline
844 & $\tau$ & $\omega$ & $\alpha$ & $\theta$ & year \\
845 \hline
846 $\tau$ &$1.000$&$-0.438$&$-0.581$&$ 0.721$&$ 0.108$\\
847 $\omega$& &$ 1.000$&$ 0.682$&$ 0.014$&$-0.021$\\
848 $\alpha$& & &$ 1.000$&$-0.081$&$ 0.030$\\
849 $\theta$& &\multicolumn{1}{c||}{---}
850 & &$ 1.000$&$-0.073$\\
851 y. & & & & &$ 1.000$\\
852 \hline
853 \end{tabular}
854 \end{table}
856 Three high-level Go players (Alexander Dinerstein 3-pro, Motoki Noguchi
857 7-dan and V\'{i}t Brunner 4-dan) have judged style of the reference
858 players.
859 The complete list of answers is in table \ref{fig:style_marks}.
860 Mean standard deviation of the answers is 0.952,
861 making the data reasonably reliable,
862 though much larger sample would of course be more desirable.
863 We have also found significant correlation between the various
864 style aspects, as shown by the Pearson's $r$ values
865 in table \ref{fig:style_marks_r}.
867 \begin{table}[!t]
868 % increase table row spacing, adjust to taste
869 \renewcommand{\arraystretch}{1.3}
870 \begin{threeparttable}
871 \caption{Expert-Based Style Aspects of Selected Professionals\tnote{1} \tnote{2}}
872 \label{fig:style_marks}
873 \centering
874 % Some packages, such as MDW tools, offer better commands for making tables
875 % than the plain LaTeX2e tabular which is used here.
876 \begin{tabular}{|c||c||c||c||c|}
877 \hline
878 {Player} & $\tau$ & $\omega$ & $\alpha$ & $\theta$ \\
879 \hline
880 Go Seigen\tnote{3} & $6.0 \pm 2.0$ & $9.0 \pm 1.0$ & $8.0 \pm 1.0$ & $5.0 \pm 1.0$ \\
881 Ishida Yoshio\tnote{4}&$8.0 \pm 1.4$ & $5.0 \pm 1.4$ & $3.3 \pm 1.2$ & $5.3 \pm 0.5$ \\
882 Miyazawa Goro & $1.5 \pm 0.5$ & $10 \pm 0 $ & $9.5 \pm 0.5$ & $4.0 \pm 1.0$ \\
883 Yi Ch'ang-ho\tnote{5}& $7.0 \pm 0.8$ & $5.0 \pm 1.4$ & $2.6 \pm 0.9$ & $2.6 \pm 1.2$ \\
884 Sakata Eio & $7.6 \pm 1.7$ & $4.6 \pm 0.5$ & $7.3 \pm 0.9$ & $8.0 \pm 1.6$ \\
885 Fujisawa Hideyuki & $3.5 \pm 0.5$ & $9.0 \pm 1.0$ & $7.0 \pm 0.0$ & $4.0 \pm 0.0$ \\
886 Otake Hideo & $4.3 \pm 0.5$ & $3.0 \pm 0.0$ & $4.6 \pm 1.2$ & $3.6 \pm 0.9$ \\
887 Kato Masao & $2.5 \pm 0.5$ & $4.5 \pm 1.5$ & $9.5 \pm 0.5$ & $4.0 \pm 0.0$ \\
888 Takemiya Masaki & $1.3 \pm 0.5$ & $6.3 \pm 2.1$ & $7.0 \pm 0.8$ & $1.3 \pm 0.5$ \\
889 Kobayashi Koichi & $9.0 \pm 1.0$ & $2.5 \pm 0.5$ & $2.5 \pm 0.5$ & $5.5 \pm 0.5$ \\
890 Cho Chikun & $9.0 \pm 0.8$ & $7.6 \pm 0.9$ & $6.6 \pm 1.2$ & $9.0 \pm 0.8$ \\
891 Ma Xiaochun & $8.0 \pm 2.2$ & $6.3 \pm 0.5$ & $5.6 \pm 1.9$ & $8.0 \pm 0.8$ \\
892 Yoda Norimoto & $6.3 \pm 1.7$ & $4.3 \pm 2.1$ & $4.3 \pm 2.1$ & $3.3 \pm 1.2$ \\
893 Luo Xihe & $7.3 \pm 0.9$ & $7.3 \pm 2.5$ & $7.6 \pm 0.9$ & $6.0 \pm 1.4$ \\
894 O Meien & $2.6 \pm 1.2$ & $9.6 \pm 0.5$ & $8.3 \pm 1.7$ & $3.6 \pm 1.2$ \\
895 Rui Naiwei & $4.6 \pm 1.2$ & $5.6 \pm 0.5$ & $9.0 \pm 0.8$ & $3.3 \pm 1.2$ \\
896 Yuki Satoshi & $3.0 \pm 1.0$ & $8.5 \pm 0.5$ & $9.0 \pm 1.0$ & $4.5 \pm 0.5$ \\
897 Hane Naoki & $7.5 \pm 0.5$ & $2.5 \pm 0.5$ & $4.0 \pm 0.0$ & $4.5 \pm 1.5$ \\
898 Takao Shinji & $5.0 \pm 1.0$ & $3.5 \pm 0.5$ & $5.5 \pm 1.5$ & $4.5 \pm 0.5$ \\
899 Yi Se-tol & $5.3 \pm 0.5$ & $6.6 \pm 2.5$ & $9.3 \pm 0.5$ & $6.6 \pm 1.2$ \\
900 Yamashita Keigo\tnote{4}&$2.0\pm 0.0$& $9.0 \pm 1.0$ & $9.5 \pm 0.5$ & $3.0 \pm 1.0$ \\
901 Cho U & $7.3 \pm 2.4$ & $6.0 \pm 0.8$ & $5.3 \pm 1.7$ & $6.3 \pm 1.7$ \\
902 Gu Li & $5.6 \pm 0.9$ & $7.0 \pm 0.8$ & $9.0 \pm 0.8$ & $4.0 \pm 0.8$ \\
903 Chen Yaoye & $6.0 \pm 1.0$ & $4.0 \pm 1.0$ & $6.0 \pm 1.0$ & $5.5 \pm 0.5$ \\
904 \hline
905 \end{tabular}
906 \begin{tablenotes}
907 \item [1] Including standard deviation. Only players where we got at least two out of tree answers are included.
908 \item [2] We consider era as one of factors when finding correlations with pattern vectors; we quantify era by taking median year over all games played by the player. Since this quantity does not fit to the table, we at least sort the players ascending by their median year.
909 \item [3] We do not consider games of Go Seigen due to him playing across several distinct Go-playing eras and thus specifically high diversity of patterns.
910 \item [4] We do not consider games of Ishida Yoshio and Yamashita Keigo for the PCA analysis since they are significant outliers, making high-order dimensions much like purely ``similarity to this player''. Takemiya Masaki has the similar effect for the first dimension, but this corresponds to common knowledge of him being an extreme proponent of anti-territorial (``moyo'') style.
911 \item [5] We consider games only up to year 2004, since Yi Ch'ang-ho was prominent representative of a balanced, careful player until then, but is regarded to have altered his style significantly afterwards.
912 \end{tablenotes}
913 \end{threeparttable}
914 \end{table}
916 \subsection{Style Components Analysis}
918 \begin{figure}[!t]
919 \centering
920 \includegraphics[width=3.75in]{style-pca}
921 \caption{PCA of per-player vectors}
922 \label{fig:style_pca}
923 \end{figure}
925 We have looked at the five most significant dimensions of the pattern data
926 yielded by the PCA analysis of the reference player set%
927 \footnote{We also tried to observe PCA effect of removing outlying Takemiya
928 Masaki. This second dimension strongly
929 correlated to territoriality and third dimension strongly correlacted to era,
930 however the first dimension remained mysteriously uncorrelated and with no
931 obvious interpretation.}
932 (fig. \ref{fig:style_pca} shows three).
933 We have again computed the Pearson's $r$ for all combinations of PCA dimensions
934 and dimensions of the prior knowledge style vectors to find correlations.
936 \begin{table}[!t]
937 % increase table row spacing, adjust to taste
938 \renewcommand{\arraystretch}{1.3}
939 \caption{Covariance Measure of Patterns and Prior Information}
940 \label{fig:style_r}
941 \centering
942 % Some packages, such as MDW tools, offer better commands for making tables
943 % than the plain LaTeX2e tabular which is used here.
944 \begin{tabular}{|c||c||c||c||c||c|}
945 \hline
946 Eigenval. & $\tau$ & $\omega$ & $\alpha$ & $\theta$ & Year \\
947 \hline
948 0.447 & {\bf -0.530} & 0.323 & 0.298 & {\bf -0.554} & 0.090 \\
949 0.194 & {\bf -0.547} & 0.215 & 0.249 & -0.293 & {\bf -0.630} \\
950 0.046 & 0.131 & -0.002 & -0.128 & 0.242 & {\bf -0.630} \\
951 0.028 & -0.011 & 0.225 & 0.186 & 0.131 & 0.067 \\
952 0.024 & -0.181 & 0.174 & -0.032 & -0.216 & 0.352 \\
953 \hline
954 \end{tabular}
955 \end{table}
957 \begin{table}[!t]
958 % increase table row spacing, adjust to taste
959 \renewcommand{\arraystretch}{1.3}
960 \caption{Characteristic Patterns of PCA Dimensions}
961 \label{fig:style_ptterns}
962 \centering
963 % Some packages, such as MDW tools, offer better commands for making tables
964 % than the plain LaTeX2e tabular which is used here.
965 \begin{tabular}{|cccc|}
966 \hline
967 PCA1 top &
968 \begin{psgopartialboard*}{(8,1)(12,6)}
969 \stone[\marktr]{black}{k}{4}
970 \end{psgopartialboard*} &
971 \begin{psgopartialboard*}{(3,1)(5,6)}
972 \stone{white}{d}{3}
973 \stone[\marktr]{black}{d}{5}
974 \end{psgopartialboard*} &
975 \begin{psgopartialboard*}{(5,1)(10,6)}
976 \stone{white}{f}{3}
977 \stone[\marktr]{black}{j}{4}
978 \end{psgopartialboard*} \\
979 $0.447 \cdot$ & $0.274$ & $0.086$ & $0.083$ \\
980 & side extension or \par 4--4 corner opening & high corner approach & high distant pincer \\
981 PCA1 bot. &
982 \begin{psgopartialboard*}{(3,1)(7,6)}
983 \stone{white}{d}{4}
984 \stone[\marktr]{black}{f}{3}
985 \end{psgopartialboard*} &
986 \begin{psgopartialboard*}{(3,1)(7,6)}
987 \stone{white}{c}{6}
988 \stone{black}{d}{4}
989 \stone[\marktr]{black}{f}{3}
990 \end{psgopartialboard*} &
991 \begin{psgopartialboard*}{(3,1)(7,6)}
992 \stone{black}{d}{4}
993 \stone[\marktr]{black}{f}{3}
994 \end{psgopartialboard*} \\
995 $0.447 \cdot$ & $-0.399$ & $-0.399$ & $-0.177$ \\
996 & low corner approach & low corner reply & low corner enclosure \\
997 \hline
998 \end{tabular}
999 \end{table}
1001 It is immediately
1002 obvious both from the measured $r$ and visual observation
1003 that by far the most significant vector corresponds very well
1004 to the player territoriality,\footnote{Cho Chikun, perhaps the best-known
1005 super-territorial player, is not well visible in the cluster, but he is
1006 positioned around $-0.8$ on the first dimension.}
1007 confirming the intuitive notion that this aspect of style
1008 is the one easiest to pin-point and also
1009 most obvious in the played shapes and sequences
1010 (that can obviously aim directly at taking secure territory
1011 or building center-oriented framework). Thick (solid) play also plays
1012 a role, but these two style dimensions have been already shown
1013 to be correlated in prior data.
1015 In other PCA dimensions correspond well to to identify and name, but there
1016 certainly is some influence of the styles on the patterns;
1017 the found correlations are presented in table \ref{fig:style_r}.
1018 (Larger absolute value means better linear correspondence.)
1020 We also list the characteristic spatial patterns of the PCA dimension
1021 extremes (table \ref{fig:style_patterns}) --- however, naive inference
1022 of characteristic patterns based on projection matrix coefficients
1023 does not work well, better methods will have to be researched.%
1024 \footnote{For example, as one of highly ranked ``Takemiya's'' PCA1 patterns,
1025 3,3 corner opening was generated, completely inappropriately;
1026 it reflects some weak ordering in bottom half of the dimension,
1027 not global ordering within the dimension.}
1029 We have not found significant correspondence for the style aspects
1030 representing aggressiveness and novelty of play; this means either
1031 these are not as well defined, the prior information do not represent
1032 them accurately, or we cannot capture them well with our chosen pattern
1033 extraction techniques.
1035 We believe that the next step
1036 in interpreting our results will be more refined prior information input
1037 and precise analysis by Go experts.
1039 Kohonen map view.
1041 \subsection{Style Classification}
1043 %TODO vsude zcheckovat jestli pouzivame stejny cas "we perform, we apply" X "we have performed, ..."
1045 Apart from the PCA-based analysis, we applied neural network (sec. \ref{neural-net})
1046 and $k$-NN classifiers (sec. \ref{knn}).
1048 To compare and evaluate both methods, we have performed $5$-fold cross validation \cite{TODO} and
1049 compared them with a~random classificator.
1050 In the $5$-fold cross-validation, we randomly divide the training set into $5$ distinct parts with comparable
1051 sizes and then iteratively use each part as a~testing set (yielding square error value), while
1052 the rest (remaining $4$ parts) is taken as a~training set. The square errors across all $5$ iterations are
1053 averaged, yielding mean square error.
1055 The results are shown in table \ref{crossval-cmp}. Second to fifth columns in the table represent
1056 mean square error of different styles (see \ref{style vectors}), $\mathit{Mean}$ is the
1057 mean square error across the styles and finally, the last column $\mathit{Comp}$
1058 represents $\mathit{Mean}_\mathit{RND} / \mathit{X}$ -- comparison of mean square error (across styles)
1059 with random classificator. To minimize the
1060 effect of random variables, all numbers were taken as an average of $30$ runs of the cross validation.
1062 \begin{table}[!t]
1063 \label{crossval-cmp}
1064 \begin{center}
1065 \caption{Comparison of style classificators}
1066 \begin{tabular}{|c|c|c|c|c|c|c|}
1067 \hline
1068 %Classifier & $\sigma_\tau$ & $\sigma_\omega$ & $\sigma_\alpha$ & $\sigma_\theta$ & Tot $\sigma$ & $\mathit{RndC}$\\ \hline
1069 %Neural network & 0.420 & 0.488 & 0.365 & 0.371 & 0.414 & 1.82 \\
1070 %$k$-NN ($k=4$) & 0.394 & 0.507 & 0.457 & 0.341 & 0.429 & 1.76 \\
1071 %Random classifier & 0.790 & 0.773 & 0.776 & 0.677 & 0.755 & 1.00 \\ \hline
1072 &\multicolumn{5}{|c|}{MSE}& \\ \hline
1073 {Classifier} & $\tau$ & $\omega$ & $\alpha$ & $\theta$ & {\bf Mean} & {\bf Comp}\\ \hline
1074 Neural network & 0.173 & 0.236 & 0.136 & 0.143 & 0.172 & 3.3 \\
1075 $k$-NN ($k=4$) & 0.156 & 0.257 & 0.209 & 0.116 & 0.184 & 3.1\\
1076 Random classifier & 0.544 & 0.640 & 0.647 & 0.458 & 0.572 & 1.0 \\ \hline
1077 \end{tabular}
1078 \end{center}
1079 \end{table}
1081 \subsubsection{Reference (Training) Data}
1082 As a~reference data, we use expert based knowledge presented in section \ref{style-vectors}.
1083 For both methods to yield comparable errors, we have rescaled style vectors to interval $[-1,1]$
1084 (since neural network's activation function has such range).
1086 % TODO presunout konkretni parametry do Appendixu? (neni jich tolik, mozna ne)
1087 \subsubsection{$k$-NN parameters}
1088 $k=4$, Weight function is $0.8^{(10*EuclideanDistance)}$
1090 \subsubsection{Neural network's parameters}
1091 $3$ layers, $23 - 30 - 4$ architecture
1094 \section{Proposed Applications}
1096 We believe that our findings might be useful for many applications
1097 in the area of Go support software as well as Go-playing computer engines.
1099 The style analysis can be an excellent teaching aid --- classifying style
1100 dimensions based on player's pattern vector, many study recommendations
1101 can be given, e.g. about the professional games to replay, the goal being
1102 balancing understanding of various styles to achieve well-rounded skill set.
1103 This was also our original aim when starting the research and a user-friendly
1104 tool based on our work is now being created.
1106 We hope that more strong players will look into the style dimensions found
1107 by our statistical analysis --- analysis of most played patterns of prospective
1108 opponents might prepare for the game, but we especially hope that new insights
1109 on strategic purposes of various shapes and general human understanding
1110 of the game might be achieved by investigating the style-specific patterns.
1112 Classifying playing strength of a pattern vector of a player can be used
1113 e.g. to help determine initial real-world rating of a player before their
1114 first tournament based on games played on the internet; some players especially
1115 in less populated areas could get fairly strong before playing their first
1116 real tournament.
1118 Analysis of pattern vectors extracted from games of Go-playing programs
1119 in light of the shown strength and style distributions might help to
1120 highlight some weaknesses and room for improvements. (However, since
1121 correlation does not imply causation, simply optimizing Go-playing programs
1122 according to these vectors is unlikely to yield good results.)
1123 Another interesting applications in Go-playing programs might be strength
1124 adjustment; the program can classify the player's level based on the pattern
1125 vector from its previous games and auto-adjust its difficulty settings
1126 accordingly to provide more even games for beginners.
1129 % An example of a floating figure using the graphicx package.
1130 % Note that \label must occur AFTER (or within) \caption.
1131 % For figures, \caption should occur after the \includegraphics.
1132 % Note that IEEEtran v1.7 and later has special internal code that
1133 % is designed to preserve the operation of \label within \caption
1134 % even when the captionsoff option is in effect. However, because
1135 % of issues like this, it may be the safest practice to put all your
1136 % \label just after \caption rather than within \caption{}.
1138 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1139 % option should be used if it is desired that the figures are to be
1140 % displayed while in draft mode.
1142 %\begin{figure}[!t]
1143 %\centering
1144 %\includegraphics[width=2.5in]{myfigure}
1145 % where an .eps filename suffix will be assumed under latex,
1146 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1147 % via \DeclareGraphicsExtensions.
1148 %\caption{Simulation Results}
1149 %\label{fig_sim}
1150 %\end{figure}
1152 % Note that IEEE typically puts floats only at the top, even when this
1153 % results in a large percentage of a column being occupied by floats.
1156 % An example of a double column floating figure using two subfigures.
1157 % (The subfig.sty package must be loaded for this to work.)
1158 % The subfigure \label commands are set within each subfloat command, the
1159 % \label for the overall figure must come after \caption.
1160 % \hfil must be used as a separator to get equal spacing.
1161 % The subfigure.sty package works much the same way, except \subfigure is
1162 % used instead of \subfloat.
1164 %\begin{figure*}[!t]
1165 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1166 %\label{fig_first_case}}
1167 %\hfil
1168 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1169 %\label{fig_second_case}}}
1170 %\caption{Simulation results}
1171 %\label{fig_sim}
1172 %\end{figure*}
1174 % Note that often IEEE papers with subfigures do not employ subfigure
1175 % captions (using the optional argument to \subfloat), but instead will
1176 % reference/describe all of them (a), (b), etc., within the main caption.
1179 % An example of a floating table. Note that, for IEEE style tables, the
1180 % \caption command should come BEFORE the table. Table text will default to
1181 % \footnotesize as IEEE normally uses this smaller font for tables.
1182 % The \label must come after \caption as always.
1184 %\begin{table}[!t]
1185 %% increase table row spacing, adjust to taste
1186 %\renewcommand{\arraystretch}{1.3}
1187 % if using array.sty, it might be a good idea to tweak the value of
1188 % \extrarowheight as needed to properly center the text within the cells
1189 %\caption{An Example of a Table}
1190 %\label{table_example}
1191 %\centering
1192 %% Some packages, such as MDW tools, offer better commands for making tables
1193 %% than the plain LaTeX2e tabular which is used here.
1194 %\begin{tabular}{|c||c|}
1195 %\hline
1196 %One & Two\\
1197 %\hline
1198 %Three & Four\\
1199 %\hline
1200 %\end{tabular}
1201 %\end{table}
1204 % Note that IEEE does not put floats in the very first column - or typically
1205 % anywhere on the first page for that matter. Also, in-text middle ("here")
1206 % positioning is not used. Most IEEE journals use top floats exclusively.
1207 % Note that, LaTeX2e, unlike IEEE journals, places footnotes above bottom
1208 % floats. This can be corrected via the \fnbelowfloat command of the
1209 % stfloats package.
1213 \section{Conclusion}
1214 The conclusion goes here.
1215 We have shown brm and proposed brm.
1217 Since we are not aware of any previous research on this topic and we
1218 are limited by space and time constraints, plenty of research remains
1219 to be done. There is plenty of room for further research in all parts
1220 of our analysis --- different methods of generating the $\vec p$ vectors
1221 can be explored; other data mining methods could be tried.
1222 It can be argued that many players adjust their style by game conditions
1223 (Go development era, handicap, komi and color, time limits, opponent)
1224 or styles might express differently in various game stages.
1225 More professional players could be consulted on the findings
1226 and for style scales calibration. Impact of handicap games on by-strength
1227 $\vec p$ distribution should be investigated.
1229 TODO: Future research --- Sparse PCA
1234 % if have a single appendix:
1235 %\appendix[Proof of the Zonklar Equations]
1236 % or
1237 %\appendix % for no appendix heading
1238 % do not use \section anymore after \appendix, only \section*
1239 % is possibly needed
1241 % use appendices with more than one appendix
1242 % then use \section to start each appendix
1243 % you must declare a \section before using any
1244 % \subsection or using \label (\appendices by itself
1245 % starts a section numbered zero.)
1249 %\appendices
1250 %\section{Proof of the First Zonklar Equation}
1251 %Appendix one text goes here.
1253 %% you can choose not to have a title for an appendix
1254 %% if you want by leaving the argument blank
1255 %\section{}
1256 %Appendix two text goes here.
1259 % use section* for acknowledgement
1260 \section*{Acknowledgment}
1261 \label{acknowledgement}
1263 We would like to thank Radka ``chidori'' Hane\v{c}kov\'{a} for the original research idea
1264 and X for reviewing our paper.
1265 We appreciate helpful comments on our general methodology
1266 by John Fairbairn, T. M. Hall, Cyril H\"oschl, Robert Jasiek, Franti\v{s}ek Mr\'{a}z
1267 and several GoDiscussions.com users. \cite{GoDiscThread}
1268 Finally, we are very grateful for detailed input on specific go styles
1269 by Alexander Dinerstein, Motoki Noguchi and V\'{i}t Brunner.
1272 % Can use something like this to put references on a page
1273 % by themselves when using endfloat and the captionsoff option.
1274 \ifCLASSOPTIONcaptionsoff
1275 \newpage
1280 % trigger a \newpage just before the given reference
1281 % number - used to balance the columns on the last page
1282 % adjust value as needed - may need to be readjusted if
1283 % the document is modified later
1284 %\IEEEtriggeratref{8}
1285 % The "triggered" command can be changed if desired:
1286 %\IEEEtriggercmd{\enlargethispage{-5in}}
1288 % references section
1290 % can use a bibliography generated by BibTeX as a .bbl file
1291 % BibTeX documentation can be easily obtained at:
1292 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1293 % The IEEEtran BibTeX style support page is at:
1294 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1295 \bibliographystyle{IEEEtran}
1296 % argument is your BibTeX string definitions and bibliography database(s)
1297 \bibliography{gostyle}
1299 % <OR> manually copy in the resultant .bbl file
1300 % set second argument of \begin to the number of references
1301 % (used to reserve space for the reference number labels box)
1302 %\begin{thebibliography}{1}
1304 %\bibitem{MasterMCTS}
1306 %\end{thebibliography}
1308 % biography section
1310 % If you have an EPS/PDF photo (graphicx package needed) extra braces are
1311 % needed around the contents of the optional argument to biography to prevent
1312 % the LaTeX parser from getting confused when it sees the complicated
1313 % \includegraphics command within an optional argument. (You could create
1314 % your own custom macro containing the \includegraphics command to make things
1315 % simpler here.)
1316 %\begin{biography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
1317 % or if you just want to reserve a space for a photo:
1319 \begin{IEEEbiography}{Michael Shell}
1320 Biography text here.
1321 \end{IEEEbiography}
1323 % if you will not have a photo at all:
1324 \begin{IEEEbiographynophoto}{John Doe}
1325 Biography text here.
1326 \end{IEEEbiographynophoto}
1328 % insert where needed to balance the two columns on the last page with
1329 % biographies
1330 %\newpage
1332 \begin{IEEEbiographynophoto}{Jane Doe}
1333 Biography text here.
1334 \end{IEEEbiographynophoto}
1336 % You can push biographies down or up by placing
1337 % a \vfill before or after them. The appropriate
1338 % use of \vfill depends on what kind of text is
1339 % on the last page and whether or not the columns
1340 % are being equalized.
1342 %\vfill
1344 % Can be used to pull up biographies so that the bottom of the last one
1345 % is flush with the other column.
1346 %\enlargethispage{-5in}
1350 % that's all folks
1351 \end{document}