A wavelet kernel for support vector machine based on frame theory

A wavelet kernel for support vector machine (SVM) based on wavelet dual frame theory and conditions of constructing SVM kernel is presented, which increases the accuracy and convergent rate of the model, and computation burden is weakened According to the wavelet kernel function and the regularization theory, a least square wavelet support vector machine (LS-WSVM) is proposed to greatly simplify the solving process of SVM. The LS-WSVM is then applied to the nonlinear system identification to test the validity of the wavelet kernel function, In logistic chaos sequence prediction, the MSE is no more than 8X10(-6) meanwhile, the MSE is not increased while increasing the predicting length. The result shows its better generalization ability. Especially, suitable for local signal analysis, signal-noise separation and detection of jumping signals with the characteristics of multi-scale interpolation and sparse variation.