From 1dda9ba458a17cc9c893640f98b163953fcb8484 Mon Sep 17 00:00:00 2001 From: Petr Baudis Date: Fri, 12 Mar 2010 01:19:27 +0100 Subject: [PATCH] tex: PCA3 patterns --- tex/gostyle.tex | 109 ++++++++++++++++++++++++++++++++++++++++++++------------ 1 file changed, 87 insertions(+), 22 deletions(-) diff --git a/tex/gostyle.tex b/tex/gostyle.tex index 2407874..fc969d1 100644 --- a/tex/gostyle.tex +++ b/tex/gostyle.tex @@ -980,20 +980,20 @@ Eigenval. & $\tau$ & $\omega$ & $\alpha$ & $\theta$ & Year \\ \begin{table}[!t] % increase table row spacing, adjust to taste -\renewcommand{\arraystretch}{1.3} +\renewcommand{\arraystretch}{2.0} \begin{threeparttable} -\caption{Characteristic Patterns of PCA Dimensions \tnote{1}} +\caption{Characteristic Patterns of PCA$_{1,2}$ Dimensions \tnote{1}} \label{fig:style_patterns} \centering % Some packages, such as MDW tools, offer better commands for making tables % than the plain LaTeX2e tabular which is used here. -\begin{tabular}{|cccc|} -\hline -PCA1 \tnote{2} & +\begin{tabular}{|ccc|} + +\hline \multicolumn{3}{|c|}{PCA$_1$ --- Moyo-oriented, thin-playing player} \\ \begin{psgopartialboard*}{(8,1)(12,6)} \stone[\marktr]{black}{k}{4} \end{psgopartialboard*} & -\begin{psgopartialboard*}{(3,1)(5,6)} +\begin{psgopartialboard*}{(1,2)(5,6)} \stone{white}{d}{3} \stone[\marktr]{black}{d}{5} \end{psgopartialboard*} & @@ -1001,9 +1001,10 @@ PCA1 \tnote{2} & \stone{white}{f}{3} \stone[\marktr]{black}{j}{4} \end{psgopartialboard*} \\ -$0.447 \cdot$ & $0.274$ & $0.086$ & $0.083$ \\ -& high corner/side opening & high corner approach & high distant pincer \\ -PCA1 \tnote{3} & +$0.274$ & $0.086$ & $0.083$ \\ +high corner/side opening & high corner approach & high distant pincer \\ + +\hline \multicolumn{3}{|c|}{PCA$_1$ --- Territorial, thick-playing player} \\ \begin{psgopartialboard*}{(3,1)(7,6)} \stone{white}{d}{4} \stone[\marktr]{black}{f}{3} @@ -1017,9 +1018,10 @@ PCA1 \tnote{3} & \stone{black}{d}{4} \stone[\marktr]{black}{f}{3} \end{psgopartialboard*} \\ -$0.447 \cdot$ & $-0.399$ & $-0.399$ & $-0.177$ \\ -& low corner approach & low corner reply & low corner enclosure \\ -PCA2 \tnote{4} \tnote{5} & +$-0.399$ & $-0.399$ & $-0.177$ \\ +low corner approach & low corner reply & low corner enclosure \\ + +\hline \multicolumn{3}{|c|}{PCA$_2$ --- Territorial, current player \tnote{2}} \\ \begin{psgopartialboard*}{(3,1)(7,6)} \stone{white}{c}{6} \stone{black}{d}{4} @@ -1034,18 +1036,76 @@ PCA2 \tnote{4} \tnote{5} & \stone{white}{f}{3} \stone[\marktr]{black}{h}{3} \end{psgopartialboard*} \\ -$0.189 \cdot$ & $-0.193$ & $-0.139$ & $-0.135$ \\ -& low corner reply \tnote{6} & high distant approach/pincer & near low pincer \\ +$-0.193$ & $-0.139$ & $-0.135$ \\ +low corner reply \tnote{3} & high distant approach/pincer & near low pincer \\ + \hline \end{tabular} \begin{tablenotes} -\item [1] We present the patterns in a simplified compact form; in reality, they are usually somewhat larger and always circle-shaped (centered on the triangled move). We omit only pattern segments that are entirely empty. -\item [2] The more frequent the shape, the more moyo-oriented and thin-playing the player. -\item [3] The more frequent the shape, the more territorial and thick-playing the player. -\item [4] The more frequent the shape, the more territorial and more current the player. -\item [5] In the second PCA dimension, we find no correlated patterns; +\item [1] We present the patterns in a simplified compact form; +in reality, they are usually somewhat larger and always circle-shaped +(centered on the triangled move). +We omit only pattern segments that are entirely empty. +\item [2] In the second PCA dimension, we find no correlated patterns; only uncorrelated and anti-correlated ones. -\item [6] As the second most significant pattern, we skip a slide follow-up pattern to this move. +\item [3] As the second most significant pattern, +we skip a slide follow-up pattern to this move. +\end{tablenotes} +\end{threeparttable} +\end{table} + +\begin{table}[!t] +% increase table row spacing, adjust to taste +\renewcommand{\arraystretch}{2.0} +\begin{threeparttable} +\caption{Characteristic Patterns of PCA$_3$ Dimension \tnote{1}} +\label{fig:style_patterns3} +\centering +% Some packages, such as MDW tools, offer better commands for making tables +% than the plain LaTeX2e tabular which is used here. +\begin{tabular}{|ccc|} + +\hline \multicolumn{3}{|c|}{PCA$_3$ --- Old-time player} \\ +\begin{psgopartialboard*}{(1,3)(5,7)} +\stone{white}{d}{4} +\stone[\marktr]{black}{c}{6} +\end{psgopartialboard*} & +\begin{psgopartialboard*}{(8,1)(12,5)} +\stone[\marktr]{black}{k}{3} +\end{psgopartialboard*} & +\begin{psgopartialboard*}{(1,1)(5,5)} +\stone[\marktr]{black}{c}{3} +\end{psgopartialboard*} \\ +$0.515$ & $0.264$ & $0.258$ \\ +low corner approach & low side/mokuhazushi opening & san-san opening \\ + +\hline \multicolumn{3}{|c|}{PCA$_3$ --- Current player} \\ +\begin{psgopartialboard*}{(3,1)(7,5)} +\stone{black}{d}{4} +\stone[\marktr]{black}{f}{3} +\end{psgopartialboard*} & +\begin{psgopartialboard*}{(1,1)(5,5)} +\stone[\marktr]{black}{c}{4} +\end{psgopartialboard*} & +\begin{psgopartialboard*}{(1,2)(5,6)} +\stone{white}{d}{3} +\stone{black}{d}{5} +\stone[\marktr]{white}{c}{5} +\end{psgopartialboard*} \\ +$-0.276$ & $-0.273$ & $-0.116$ \\ +low corner enclosure & 3-4 corner opening \tnote{2} & high approach reply \\ + +\hline +\end{tabular} +\begin{tablenotes} +\item [1] We cannot use terms ``classic'' and ''modern'' in case of PCA$_3$ +since the current patterns are commonplace in games of past centuries +(not included in our training set) and many would call a lot of the old-time patterns +modern inventions. Perhaps we can infer that the latest 21th-century play trends abandon +many of the 20th-century experiments (lower echelon of our by-year samples) +to return to the more ordinary but effective classic patterns. +\item [2] At this point, we skip two patterns already shown elsewhere: +{\em high side/corner opening} and {\em low corner reply}. \end{tablenotes} \end{threeparttable} \end{table} @@ -1071,13 +1131,18 @@ the found correlations are all presented in table \ref{fig:style_r}. (Larger absolute value means better linear correspondence.) We also list the characteristic spatial patterns of the PCA dimension -extremes (table \ref{fig:style_patterns}) --- however, naive inference -of characteristic patterns based on projection matrix coefficients +extremes (tables \ref{fig:style_patterns}, \ref{fig:style_patterns3}), determined by their coefficients +in the PCA projection matrix --- however, such naive approach has limited reliability, better methods will have to be researched.% \footnote{For example, as one of highly ranked ``Takemiya's'' PCA1 patterns, 3,3 corner opening was generated, completely inappropriately; it reflects some weak ordering in bottom half of the dimension, not global ordering within the dimension.} +We do not show the other pattern features since they carry no useful +information in the opening stage.% +\footnote{The board distance feature can be useful in some cases, +but here all the spatial patterns are big enough to reach to the edge +on their own.} We have not found significant correspondence to the style aspects representing aggressiveness and novelty of play; this means either -- 2.11.4.GIT