Cross-validation based weights and structure determination of Chebyshev-polynomial neural networks for pattern classification

• Two neural networks are constructed and investigated for pattern classification.
• The proposed neural networks are of low computational complexity.
• Two proposed WASD algorithms can obtain proper structures of neural networks.
• The neural networks with WASD achieve high classification accuracy.
• The MOCPNN with WASD achieves strong robustness on classification.

This paper first proposes a new type of single-output Chebyshev-polynomial feed-forward neural network (SOCPNN) for pattern classification. A new type of multi-output Chebyshev-polynomial feed-forward neural network (MOCPNN) is then proposed based on such an SOCPNN. Compared with multi-layer perceptron, the proposed SOCPNN and MOCPNN have lower computational complexity and superior performance, substantiated by both theoretical analyses and numerical verifications. In addition, two weight-and-structure-determination (WASD) algorithms, one for the SOCPNN and another for the MOCPNN, are proposed for pattern classification. These WASD algorithms can determine the weights and structures of the proposed neural networks efficiently and automatically. Comparative experimental results based on different real-world classification datasets with and without added noise prove that the proposed SOCPNN and MOCPNN have high accuracy, and that the MOCPNN has strong robustness in pattern classification when equipped with WASD algorithms.