MCA EXIN NEURON - Neural-based Orthogonal Data Fitting: The EXIN Neural Networks - page 55

−a ( t ) S neuron ( w ( t ) , x ( t ))

w ( t + 1)

w ( t )

Figure 2.3 Evolution of the weight vector during updating.

w 2

z 3

initial
conditions

weight space

w 1

w 3

Figure 2.4 Dynamic behavior of the weights for MCA EXIN, LUO, OJAn, and OJA (for
particular initial conditions): three-dimensional case.

4. By increasing the modulus, the fluctuations push the weight to another
critical point, and so on until ∞ .

This analysis is illustrated in Figure 2.4 for the three-dimensional case.
In the remaining part of this section, the divergence is studied in further detail
and the sudden divergence phenomenon is illustrated.

2.6.2.1 OJAn, LUO, MCA EXIN, and the General Case All the analysis
above justifies the following fundamental theorem:

Theorem 68 (MCA Divergence) LUO, OJAn, and MCA EXIN do not converge.
MCA EXIN has the slowest divergence; LUO has the fastest divergence.