Neural networks - Signals, Processes, and Systems - page 447

• Eventually, the learning process has to be cancelled. Two bounds exist for
this matter: the amount of epochs given in the menu and the undercut of a
quality factor . The error after each epoch is the sum of deviations between
network exit and nominal value. If this sum respectively the averaged sum
per neuron is smaller than the quality factor bound, the training is
cancelled.

Because of standardization and the strong dependency from training data,
it is very difficult or nearly impossible to specify a reasonable quality
factor. As a precaution, the default always represents a very small value
(0,003). In addition, a cancellation takes place when reaching a testing
error minimum (see below).

Which test pattern process is the ideal one?

To make it short: the ideal test process doesn´t exist. The learning- and test pattern process
should - considering a bigger range - steadily decrease..

If the default 2500 epochs are reached, the training is cancelled. If 10000 epochs are
approved, as a general rule the curve shape of the learning pattern errors will not differ,
except for the fact, that the error over every learning pattern might become even smaller.

The curve shape of the test pattern error - because of the validation with the test patterns-
at first is also permanently decreasing. After that, however, there is a minimum,
depending in the first place on the quality of the training data (see Illustration 286), from
where the curve shape increases.

The curve shape of the test pattern error increasing after the
minimum can be interpreted as a decrease of the ability of the
network to generalize .

The relatively best network configuration with the present start initialization and the
randomly chosen test data thus is the process minimum of the test pattern error. In order
to be recognized objectively, the training is cancelled after 500 epochs after this
minimum, given, no other minimum appears. The network configuration included inside
this minimum is saved.

Project: pattern recognition of the signals of a function generator
To create the different project steps transparently, a pattern recognition initially appearing
to be rather simple is chosen. Four periodic signals - sinus, triangle, rectangle and
sawtooth - of equal frequency and amplitude are to be distinguished.

This task above provides nearly ideal training data. Illustration 288 shows their gathering
as well as parts of the *.nnd and *.nn file. A closer look reveals a striking characteristic:
sinus signal and triangle signal are quite similar, in the time range as well as in the
frequency range (Illustration 31 in chapter 2; the amplitudes of the odd higher harmonics
of the triangle change with 1/n 2 ).