GENERALIZATION OF LINEAR REGRESSION PROBLEMS - Neural-based Orthogonal Data Fitting: The EXIN Neural Networks - page 200

with a comparison of the neurons presented in [22]. As in Section 5.7.2, the only
comparable results in [22, Ex. 3] have a settling time of about 250 ns. The initial
conditions are null (see Section 5.7.2 for the DLS case). Every batch is composed
of the coefficients of the five equations. The learning rate for the nonaccelerated
GeTLS EXIN is α( t ) = α 0 / t γ . The discrete-time sequential (online) linear neuron
in [22, Fig. 7] has a settling time of more than 40 ms for the OLS and TLS
problems. The continuous-time batch linear neuron in [22, Fig. 6] reaches a
good accuracy for the OLS and TLS problems after about 0.4 ms. The results
for the GeTLS EXIN, shown in Table [5.4], corresponding to the same accuracy
of the MATLAB results, are far better than the previous ones, especially for
its accelerated versions (recall Remark 40). The same considerations of Section
5.7.2 can be repeated here. About the DLS estimation, the classical methods and
the DLS scheduling EXIN are compared. The Householder method gives the
solution x = [1 . 1200, 0 . 1867] T . For the weighted TLS method, the parameter α
has been varied between 1 and 250 in steps of 1. The variation of x 1 and x 2 vs.
α is shown in Figure 5.27. For α ≈ 200 the solution is x = [1 . 1200, 0 . 1867] T
and does not change for larger α . Then a not too large value of α is enough
for a good accuracy of the DLS solution. Figure 5.28 shows the plot of the
weights of the sequential GeTLS EXIN with hyperbolic scheduling. The initial
conditions are null. The settling time is about 2.5 ms (1 itereration = 0.01 ms).
The learning rate is held constant at the value 0.5 for the first 130 iterations and
at the value 0.001 after iteration 300. The two constant values are connected by a
third-degree polynomial. The transient and the accuracy are excellent. Figure 5.29
Figure 5.28 Plot of the weights of DLS scheduling EXIN for the benchmark problem
(hyperbolic scheduling and null initial conditions). ( See insert for color representation of the
figure .)