3.3 Normalisation

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3.3 Normalisation

$\begin{displaymath} S_{Total}=\frac{S}{S_{0}},\,\, G_{Total}=\frac{G}{G_{0}}\end{displaymath}$

(1)

$\begin{displaymath} S_{\sigma_{Total}}=\sqrt{\frac{S_{0}^{2}\sigma_{s}^{2}+S^{2}\sigma_{s0}^{2}}{S_{s0}^{4}}}\end{displaymath}$

(2)

$\begin{displaymath} G_{\sigma_{Total}}=\sqrt{\frac{G_{0}^{2}\sigma_{g}^{2}+G^{2}\sigma_{g0}^{2}}{G_{g0}^{4}}}\end{displaymath}$

(3)

where:

: Specificity using training set
: Generalisation using training set
$S_{0}$ : Specificity using pseudo training set
$G_{0}$ : Generalisation using pseudo training set
$\sigma_{s}$ : standard error of
$\sigma_{g}$ : standard error of
$\sigma_{s0}$ : standard error of $S_{0}$
$\sigma_{g0}$ : standard error of $G_{0}$

$\includegraphics[% scale=0.4]{EPS/Normalisation_Framework/normalisation_framework.eps}$

Figure x: The framework of normalisation. Two sets of training data, one which is real and one which is synthesised are compared to model-generated examples.

$\includegraphics[% scale=0.23]{EPS/Normalisation_Brain/real_training_data_gen.eps}$ $\includegraphics[% scale=0.23]{EPS/Normalisation_Brain/synthesised_training_data_gen.eps}$

Figure x: Comparison between the Generalisation ability derived from an original data set and a pseudo training set, as function of the number of model examples.

$\includegraphics[% scale=0.25]{EPS/Normalisation_Brain/normalised_data_gen.eps}$ $\includegraphics[% scale=0.25]{EPS/Normalisation_Brain/spec_normalised_corrected.eps}$

Figure x: Normalised Generalisation ability and Specificity as a function of the number of model examples.

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Roy Schestowitz 平成17年6月23日