Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1997. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 24)

HOFFMANN, M. and VÁRADY, L., Free-form curve design by neural networks

Free-form curve design by neural networks 101 Xi x

2 Figure 1. The training of the network is figured out by presenting data vectors P{ to the input layer of the network whose connection weights Wij are initially chosen as random values. Compute the Euclidean distance between the input point P\ (^1,^2) and the output neurons oi (wn

, ) with di — i 3=1 Wij)

2 The neuron c with the minimum distance will be activated, where d

c = minjcij} = 1,

. . ., m). The update of the weights Wij associated to the neurons is only performed within a neighbourhood N

c(t) of c. This neighbourhood is reduced with training time t. The update follows the equation = + (i = 1,..., m; j = 1, 2) where Aw\f = T,(t){

X

j - w\f) and v{t) = Vo(l~ , where te[0,T] Here rj(t) represents a time-dependent learning rate which is decreasing in time. The term can be chosen as a Gaussian function.