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Exercises 24 1

5.14 Consider a set of three points X=(x, x,E % , i=1, 2, 3).
a) Show that Xis not pseudo-shattered by the class of linear functions F (see Figure
5.35).
b) Show that X is pseudo-shattered by the class of quadratic functions Q=( (x,j(x) =
ax2+ b);a, b~ 31 1.

5.15 Using an MLP approach, determine which shares of the StockExchange dataset are best
predicted one-day ahead, using features LISBOR and USD.

5.16 Design an RBF classifier for the three classes of cork stoppers, using features ART,
PRM, NG and RAAR. Compare the solution obtained with the one derived in Exercise
5.7, using ROC curve analysis.
5.17 Train the MLP18:22:10 classifier for the CTG data, described in section 5.7.1, with the
back-propagation algorithm. Compare the results with those shown in Table 5.7. What
is the lower bound of the number of training samples needed for training and the VC
dimension, assuming hard-limiting activation functions?

5.18 Design an MLP classifier for the CTG data for the three classes N, S and P with a
reduced feature set. Use the conjugate-gradient method for training.
5.19 Train the MLP classifier from the previous exercise with the genetic algorithm
approach (use the NeuroGenetic program). Compare the solution obtained with the one
from the previous exercise, regarding classification performance and convergence time.

5.20 Determine the progress of the conjugate-gradient method for the error surfaces shown
in Figures 5-8b and 5-9b by determining the successive minima and gradients at those
points.
5.21 Design a two-layer MLP for classification of the Rocks data into three classes: granites,
limestones and marbles. Use features SiO2, CaO and RMCS, and perform the training
with the conjugate-gradient and genetic algorithm methods.

5.22 Foetal weight estimation is also clinically relevant when approached as a classification
task. Design an MLP classifier for the foetal weight dataset, considering the classes
corresponding to the following weight intervals (in grams):
a) w,=below 1000; q=[1000, 1500[; @=[1500, 3000[; w4=[3000, 45001; os=above
4500.
b) o,=below 2000 (too low); q=[2000,4000]; &=above 4000.

5.23 Design an RBF network with Gaussian kernel for the same Rocks data classification as
in the previous exercise. Compare both solutions, using scatter plots with the class
boundaries determined by the classifiers.

5.24 Determine the optimal SVM hyperplane for a data set as in the example of Figure 5.44,
the only difference being that point x3 is now x3=(0, 1).