Multiresolution Neural Networks Based on Immune Particle Swarm Algorithm

Inspired by the theory of multiresolution analysis (MRA) of wavelets and artificial neural networks, a multiresolution neural network (MRNN) for approximating arbitrary nonlinear functions is proposed in this paper. MRNN consists of a scaling function neural network (SNN) and a set of sub-wavelet neural networks, in which each sub-neural network can capture the specific approximation behavior (global and local) at different resolution of the approximated function. The structure of MRNN has explicit physical meaning, which indeed embodies the spirit of multiresolution analysis of wavelets. A hierarchical construction algorithm is designed to gradually approximate unknown complex nonlinear relationship between input data and output data from coarse resolution to fine resolution. Furthermore, A new algorithm based on immune particle swarm optimization (IPSO) is proposed to train MRNN. To illustrate the effectiveness of our proposed MRNN, experiments are carried out with different kinds of wavelets from orthonormal wavelets to prewavelets. Simulation results show that MRNN provides accurate approximation and good generalization.