Approximation of chaotic shapes with tree-structured neural networks

The approximation of highly irregular decision regions is a challenging problem in pattern recognition and classification. Existing neural networks require many neurons for approximating irregular decision regions. A new tree-structured neural network algorithm is proposed that does not suffer from this limitation. The network approximates irregular regions parsimoniously by using receptive fields having a special overlapping structure The performance of the proposed network is evaluated on an approximation task involving a highly irregular decision region defined by the Mandelbrot set. The results show that the tree-structured neural network approximates decision regions much more parsimoniously than Kohonen and reduced Coulomb-potential networks