Constructive neural networks with piecewise interpolation capabilities for function approximations

This paper proposes a constructive neural network with a piecewise linear or nonlinear local interpolation capability to approximate arbitrary continuous functions. This neural network is devised by introducing a space tessellation which is a covering of the Euclidean space by nonoverlapping hyperpolyhedral convex cells. In the proposed neural network, a number of neural network granules (NNG´s) are processed in parallel and repeated regularly with the same structures. Each NNG does a local mapping with an interpolation capability for a corresponding hyperpolyhedral convex cell in a tessellation. The plastic weights of the NNG can be calculated to implement the mapping for training data; consequently, this reduces training time and alleviates the difficulties of local minima in training. In addition, the interpolation capability of the NNG improves the generalization for the new data within the convex cell. The proposed network requires additional neurons for tessellation over the standard multilayer neural networks. This increases the network size but does not slow the retrieval response when implemented by parallel architecture