Constructive neural networks with piecewise interpolation capabilities for function approximations
- 1 January 1994
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Neural Networks
- Vol. 5 (6), 936-944
- https://doi.org/10.1109/72.329691
Abstract
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.Keywords
This publication has 12 references indexed in Scilit:
- On learning the derivatives of an unknown mapping with multilayer feedforward networksNeural Networks, 1992
- Representation of functions by superpositions of a step or sigmoid function and their applications to neural network theoryNeural Networks, 1991
- DEFAnet—A deterministic neural network concept for function approximationNeural Networks, 1991
- Approximation capabilities of multilayer feedforward networksNeural Networks, 1991
- Approximation theory and feedforward networksNeural Networks, 1991
- A simple method to derive bounds on the size and to train multilayer neural networksIEEE Transactions on Neural Networks, 1991
- Bounds on the number of hidden neurons in multilayer perceptronsIEEE Transactions on Neural Networks, 1991
- The self-organizing mapProceedings of the IEEE, 1990
- Self-organizing network for optimum supervised learningIEEE Transactions on Neural Networks, 1990
- Identification and control of dynamical systems using neural networksIEEE Transactions on Neural Networks, 1990