Neural Network Toolbox

Post-Training Analysis (postreg)

The performance of a trained network can be measured to some extent by the errors on the training, validation and test sets, but it is often useful to investigate the network response in more detail. One option is to perform a regression analysis between the network response and the corresponding targets. The routine postreg is designed to perform this analysis.

The following commands illustrate how we can perform a regression analysis on the network that we previously trained in the early stopping section.

• a = sim(net,p);
  [m,b,r] = postreg(a,t)
  m =
      0.9874
  b =
     -0.0067
  r =
      0.9935
  

Here we pass the network output and the corresponding targets to postreg. It returns three parameters. The first two, m and b, correspond to the slope and the y-intercept of the best linear regression relating targets to network outputs. If we had a perfect fit (outputs exactly equal to targets), the slope would be 1, and the y-intercept would be 0. In this example, we can see that the numbers are very close. The third variable returned by postreg is the correlation coefficient (R-value) between the outputs and targets. It is a measure of how well the variation in the output is explained by the targets. If this number is equal to 1, then there is perfect correlation between targets and outputs. In our example, the number is very close to 1, which indicates a good fit.

The following figure illustrates the graphical output provided by postreg. The network outputs are plotted versus the targets as open circles. The best linear fit is indicated by a dashed line. The perfect fit (output equal to targets) is indicated by the solid line. In this example, it is difficult to distinguish the best linear fit line from the perfect fit line, because the fit is so good.

Principal Component Analysis (prepca, trapca)

Sample Training Session

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