Neural networks based prediction of geometrical properties with reduced mapping nonlinearity

The present paper examines how the training process of a Multilayer Feedforward Networks(MFN) can be facilitated when the nonlinearity (distribution angle CY. and distribution gradient P) of training samples is reduced. The model problem is the prediction of certain geometrical properties based on inhomogeneous planar shapes. Such type of problem is of interest in a CAD environment for the approximation of geometry related and CPU-intensive computations. In the numerical experiments, inhomogeneous planar shapes are collected and represented by the FPF descriptors. Training samples are formulated with three types of scaling schemes: 1) using the original aspect ratio of the FOURIER-POLAR-FOURIER (FPF) descriptors, 2 ) scaling the aspect ratio to unity, (i.e., to yield a hyper-cube), and 3 ) scaling the aspect ratio so that the mapping nonlinearity is minimized. Results of numerical experiments reconfirmed that the mapping nonlinearity, CY. and p, can reliably predict the empirical trainability. In addition, with the current test problem, the trainability is improved noticeably when the training object is scaled to a hyper-cube.