Page 157 - Computational Colour Science Using MATLAB

144 CHARACTERIZATION OF PRINTERS

Figure 9.1 Schematic diagram for an MLP. The solid lines represent weighted connections
between the processing units (*)

the current set of weights) is computed, and the values of the weights are
modified to reduce this error. This process is repeated for each input–output pair
in the training set and the presentation of the whole training set in this way is
known as a training epoch. Training may require thousands or even hundreds of
thousands of epochs and typically the training procedure is very computationally
intensive. However, at the end of the training period the values of the weights are
fixed. During the testing mode, input vectors are presented to the network and
output vectors are computed. The performance of the network in testing mode
using the data from the training set is known as the training error. A common
problem with MLPs is that they are prone to over-fitting the training data. As the
number of hidden layers or units in the network increases, the training error
should decrease. In the limit a sufficiently complex MLP can produce a training
error of zero; such a network, however, may exhibit poor generalization
performance. Generalization is the ability of the network to perform using data
that was not used during the training period. A second data set, known as a
testing data set, is therefore used to determine the testing error. Of course, the
training and testing data sets should be drawn from the same population so that
they both represent, in a statistical sense, the problem being addressed by the
network.