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302 Appendix B. CD Tools

8.3 Design Set Size

The PR Size program is intended to provide some guidance to the PR designer on
the choice of the appropriate system complexity, given the design set size. It has
the following modules:

SC Size (Statistical Classifier Design)

Displays a picture box containing graphics of the following variables, for a two-
class linear classifier with specified Battacharrya distance and for several values of
the dimensionality ratio, nld:

Bayes error;
Expected design set error (resubstitution method);
Expected test set error (holdout method).

Both classes are assumed to be represented by the same number of patterns per
class, n.
The user only has to specify the dimension d and the square of the Battachanya
distance (computable by several statistical software products).
For any chosen value of nld, the program also displays the standard deviations
of the error estimates when the mouse is clicked over a selected point of the picture
box.
The expected design and test set errors are computed using the formulas
presented in the work of Foley (1972) mentioned in the bibliography of Chapter 4.
The formula for the expected test set error is an approximation formula, which can
produce slightly erroneous values, below the Bayes error, for certain nld ratios.

NN Size (Neural Network Design)
Displays tables of the following values, for a two-class two-layer MLP and for a
user-specified interval of the number of hidden nodes, h:

- Number of neurons.
- Number of weights (including biases).
- Lower bound of the Vapnik-Chervonenkis dimension (formula 5-52).
- Upper bound of the Vapnik-Chervonenkis dimension (formula 5-56).
- Lower bound of learning set size needed for generalization (formula 5-53).
- Upper bound of learning set size sufficient for generalization (formula 5-56a).

The user has to specify the dimension, d, corresponding to the number of MLP
inputs, the training set error and the confidence level of the training set error.

Author: JP Marques de Sa, Engineering Faculty, Oporto University.