Page 38 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

26 Chapter 1

Figure 1-11 ANN Algorithm Illustration

The slope computed at point 2 in the figure is negative. Suppose if the
weight vector corresponding to the point 2 is treated as current weight vector
assumed, the next best value (i.e) global point is at right side of it. Similarly
if the slope is positive, next best value is left side of the current value. This
can be seen from the graph. The slope at point 3 is a positive. The best value
(i.e) global minimum is left of the current value.
Thus to obtain the best value of the weight vector. Initialize the weight
vector. Change the weight vector iteratively. Best weight vector is obtained
after finite number of iteration. The change in the weight vector in every
iteration is represented as ‘ΔW’.

(i.e.) W (n+1) =W (n) + ΔW (n+1)

th
W(n+1) is the weight vector at (n+1) iteration W(n) is the weight vector
th
th
at n iteration and ΔW(n+1) is the change in the weight vector at (n+1)
iteration.
The sign and magnitude of the ‘ΔW’ depends upon the direction and
magnitude of the slope of the cost function computed at the point
corresponding to the current weight vector.