From 3758e043a4b6618cab2dd9e840b70e147a074c36 Mon Sep 17 00:00:00 2001
From: Petr Baudis
Date: Tue, 9 Mar 2010 20:50:18 +0100
Subject: [PATCH] tex: Draft text for PCA analysis

tex/gostyle.tex  21 +++++++++++++++++
1 file changed, 17 insertions(+), 4 deletions()
diff git a/tex/gostyle.tex b/tex/gostyle.tex
index 0aaf5d3..6e8dcba 100644
 a/tex/gostyle.tex
+++ b/tex/gostyle.tex
@@ 768,10 +768,23 @@ at the ranks, discarding the differences between various systems and thus increa
error in our model.\footnote{Since
our results seem satisfying, we did not pursue to try another collection}
PCA analysis yielded X, chisquare test blabla...

We then tried to apply the NN classifier with linear output function on the dataset
and that yielded Y (see fig. Z), with MSE abcd.
+First, we have created a single pattern vector for each rank, from 30k to 4d;
+we have performed PCA analysis on the pattern vectors, achieving nearperfect
+rank correspondence in the first PCA dimension\footnote{The eigenvalue of the
+second dimension was four orders of magnitude smaller, with no discernable
+structure revealed within the lowerorder eigenvectors.}
+(chisquare test TODO).
+(Figure TODO.) Using the eigenvector position directly for classification
+of players within the test group yields MSE TODO, thus providing
+reasonably satisfying accuracy.
+
+To further enhance the strength estimator accuracy,
+we have tried to train a NN classifier on our train set, consisting
+of one $(\vec p, {\rm rank})$ pair per player  we use the pattern vector
+for activation of input neurons and rank number as result of the output
+neuron. We then proceeded to test the NN on perplayer pattern vectors built
+from the games in the test set, yielding MSE of TODO with TODO games per player
+on average.
\section{Style Components Analysis}

2.10.5.GIT