Annexe 2 - Statistical functions for validation of the SANNs
x(p) is the generic output component for the p-th input pattern, and the correspondent
target is t(p). M is the number of patterns considered for the statistical measure.
Root Mean Squared Error (RMSE), evaluating the squared root of the semi-mean of the squared prediction errors:
1M
RMSE =
2M∑ ∑( x(p )-t ( p ))2
Ï p=1
Normalized Root Mean Squared Error (NMSE), evaluating the squared root of the mean of the squared prediction
errors, where target and output values was before normalized between 0 and 1:
1M
NMSE = λ--∑
VM z^1
Ï p=1
x(p) - min k {x(k)}
min k {x(k)}- max k {x(k)}
t(p) - min k {t(k)} J ∣
min k {t(k)}- max k {t(k)}JJ
Real Error (ERR) evaluating the mean of the prediction error:
1M
ERR = -M ∑(χ ( p ) -1 ( p )) ■
M p =1
Relative Error (ABSERR) evaluating the mean of the absolute prediction errors:
1M
ABSERR = -- ∑ ∣x( p ) -1 ( p )∣ .
M p =1
Squared R (R2), evaluating the squared of the linear correlation coefficient between target and prediction values:
R2
M (( ( 1 M Y ∑ *p)-lM∑x(k)J p=1Vk k k=1 jJ |
ʌ 2 ( ( 1 M Yfl k t ( p )-k Mi∑;( k ) JJJ | |
U |
2 M ( ( 1 M ll ∑xp)-l M ∑x(k)J 4 |
2J M( (1 M ll J ∑ t(p )-l -M ∑t ( k ) J |
20
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