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, chi-square 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 near-perfect +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 lower-order eigenvectors.} +(chi-square 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 per-player 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} -- 2.11.4.GIT