5.9. EXERCISES AND PROJECTS 195
(c) Using the training and test data obtained in (a) and (b), retrain
and test a single-hidden-layered neural network with linear functions.
Compare the performance of this neural network with that using
sigmoidal functions. Can the performance be improved?
(d) For a two-hidden-layered neural network, repeat (a), (b), and (c).
Discuss issues pertaining to training time and accuracy in function
approximation.
(e) Repeat items (a), (b), (c), and (d) for the function
y 2 =sin(πx 1 )cos(0. 5 πx 2 )
- A set of six patterns from two classes are specified as follows:
n
[3,2]T,[1,−2]T,[− 2 ,0]T
o
:Class 1
n
[2,1]T,[0,−1]T,[− 1 ,2]T
o
:Class 2
(a) Is this a linearly separable problem?
(b) Design and train a single-hidden-layered neural network with linear
activation units.
(c) From the training patterns, generate a set of 20 test patterns that are
±10%of the nominal values. How does the trained neural network
perform?
(d) Augment the original set of training patterns with the set of 20 test
patternsgeneratedinstep(b)andretraintheneuralnetwork. For
a new set of test patterns, similar to that obtained in step (c), how
does the neural network perform?
(e) Show whether the performance can be improved by increasing the
number of hidden layers.
(f) Show whether the performance can be improved if the linear activa-
tion units were replaced by bipolar or unipolar sigmoidal functions.
(g) What are the consequences of choosing to adopt (e) or (f) in thefinal
design? Which design would you adopt and why?
The student is urged to take on more creative studies on how neural net-
works can be used in real-world applications. In the following, we pro-
vide projects that we consider challenging for the beginner, and hope that
such projects can be a motivation to examine more advanced approaches
to neural network-based applications. Note that there is quite a bit of di-
versity and room for exploration.
12.Project: The purpose of this project is to develop an aid for the blind in
recognizing street-crossing signals. In principle, the system would consist
of a miniature camera worn by the individual in a manner that would allow
