From ec3157746eb8d90a2fdeb87db36b1e12e77f19f3 Mon Sep 17 00:00:00 2001 From: Petr Baudis Date: Thu, 11 Mar 2010 00:12:38 +0100 Subject: [PATCH] tex: PCA-style r-table --- tex/gostyle.tex | 40 +++++++++++++++++++++++++++++++++++++--- 1 file changed, 37 insertions(+), 3 deletions(-) diff --git a/tex/gostyle.tex b/tex/gostyle.tex index 1190b15..d5559f9 100644 --- a/tex/gostyle.tex +++ b/tex/gostyle.tex @@ -881,6 +881,27 @@ obvious interpretation.} We have again computed the Pearson's $r$ for all combinations of PCA dimensions and dimensions of the prior knowledge style vectors to find correlations. +\begin{table}[!t] +% increase table row spacing, adjust to taste +\renewcommand{\arraystretch}{1.3} +\caption{Covariance Measure of Patterns and Prior Information} +\label{fig:style_r} +\centering +% Some packages, such as MDW tools, offer better commands for making tables +% than the plain LaTeX2e tabular which is used here. +\begin{tabular}{|c||c||c||c||c||c|} +\hline +Eigenval. & $\tau$ & $\omega$ & $\alpha$ & $\theta$ & Year \\ +\hline +0.447 & {\bf -0.530} & 0.323 & 0.298 & {\bf -0.554} & 0.090 \\ +0.194 & {\bf -0.547} & 0.215 & 0.249 & -0.293 & {\bf -0.630} \\ +0.046 & 0.131 & -0.002 & -0.128 & 0.242 & {\bf -0.630} \\ +0.028 & -0.011 & 0.225 & 0.186 & 0.131 & 0.067 \\ +0.024 & -0.181 & 0.174 & -0.032 & -0.216 & 0.352 \\ +\hline +\end{tabular} +\end{table} + It is immediately obvious both from the measured $r$ and visual observation that by far the most significant vector corresponds very well @@ -891,14 +912,27 @@ confirming the intuitive notion that this aspect of style is the one easiest to pin-point and also most obvious in the played shapes and sequences (that can obviously aim directly at taking secure territory -or building center-oriented framework). +or building center-oriented framework). Thick (solid) play also plays +a role, but these two style dimensions have been already shown +to be correlated in prior data. -Other PCA dimensions are far less to identify and name, but there +In other PCA dimensions correspond well to to identify and name, but there certainly is some influence of the styles on the patterns; -the found correlations are presented in table \ref{fig:style_chisq}. +the found correlations are 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}). +We have not found significant correspondence for the style aspects +representing aggressiveness and novelty of play; this means either +these are not as well defined, the prior information do not represent +them accurately, or we cannot capture them well with our chosen pattern +extraction techniques. + +We believe that the next step +in interpreting our results will be more refined prior information input +and precise analysis by Go experts. + Kohonen map view. \subsection{Style Classification} -- 2.11.4.GIT