Date: Feb 7, 2013 6:45 AM
Author: Greg Heath
Subject: Re: ANN_Error Goal
"Suresh" wrote in message <email@example.com>...
> How to decide the value of Error goal while training a neural network for different pattern recognition problems ?
Unfortunately, there is no analytic relationship between the discontinuous classification error rate Nerr/N and continuous error (target-output). Therefore, classifiers are usually trained to minimize the continuous mean-squared-error even though low classification error rate is the ultimate goal.
Subsequently, the same rule is used for regression with O-dimensional targets and classification with O = c classes where the target matrix contains columns of the c-dimensional unit matrix eye(c). In each case the data provides Neq equations
Neq = N*O
to estimate Nw unknown weights. The resulting estimation degree-of-freedom is
Ndof = Neq-Nw
The NAIVE MODEL assumes that the output is a constant equal to the mean of the
y00 = repmat(mean(target'),1,N));
Nw00 = O % size(y00,1)
Ndof00 = Neq-O % (N-1)*O
The resulting biased mse is
MSE00 = sumsqr((target-y00)/Neq
MSE00 = mean(var(target',1)) % Proof for reader
The corresponding unbiased mse that is "a"djusted for the loss of degrees of freedom caused by using the same data to estimate the Nw00 weights is
MSE00a = sumsqr((target-y00)/Ndof00
MSE00a = mean(var(target')) % Proof for reader
For more sophistcated models, the goal is to account for as much of the target data variance as possible.This is quantified by the normalized quantities
NMSE = MSE/MSE00
NMSEa = MSEa/MSE00a
with the ultimate design goal of 0 and a 100% representation of the target data variance.
Statisticians use the R-squared quantities (http://en.wikipedia.org/wiki/Coefficient_of_determination)
R2 = 1 - NMSE
R2a = 1 - NMSEa
with the ultimate design goal of 1 and a 100% representation of the target data variance.
I use the more practical design goal of R2a = 0.99 and a 99% unbiased representation of the unbiased target data variance. This yields
= MSEgoal = 0.01*Ndof*MSE00a/Neq % Proof for reader =
For a feedforward NEURAL NET model with I=H-O node topology,
Nw = (I+1)*H+(H+1)*O
net.trainParam.goal = MSEgoal;
Hope this helps.
P.S. The DOF corrections are only for the training data used to directly estimate
the weights. The corrections are not needed for nontraining validation and test data.