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Appendix B. CD Tools 303

B.4 Error Energy

The Error Energy.xl file allows the inspection of error energy surfaces
corresponding to several LMS discriminants, including the possibility of inspecting
the progress of a gradient descent process for one of the examples (iterations
performed along the columns).
The following worksheets, exemplifying different LMS situations, are included:

minglob
Error energy surface for an LMS discriminant with 2 target values (-1, l), with
only a global minimum. There are two variable weights, one with values along
the rows of column A, the other with values along columns B 1 to B 1 1.

minglob2
Similar to minglob for an error energy surface with two global minima,
corresponding to 3 target points (1,0, 1).

minloc
Similar to minglob2 with the possibility of positioning the "3rd point" in order
to generate error energy surfaces with local minima (see section 5.2, Figure
5.9).

minloc(zoom), minloc(zooml)
Zoomed areas of minloc for precise minima determination.

perceptron
Similar to rninglob using the perceptron learning rule.
ellipt-error
Ellipsoidal error surface (a2+pb2-2a-qb+l), including the possibility for the
user to inspect the progress of gradient descent, by performing iterations along
the columns, namely by specifying the initial values for the weights and the
learning rate.
The worksheet columns are labelled as:
eta Learning rate
a(new), b(new) New weight values
dE/da, dE/db Error derivatives
da db Weight increments

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