Online chaotic time series prediction using unbiased composite kernel machine via Cholesky factorization

The kernel method has proved to be an effective machine learning tool in many fields. Support vector machines with various kernel functions may have different performances, as the kernels belong to two different types, the local kernels and the global kernels. So the composite kernel, which can bring more stable results and good precision in classification and regression, is an inevitable choice. To reduce the computational complexity of the kernel machine's online modeling, an unbiased least squares support vector regression model with composite kernel is proposed. The bias item of LSSVR is eliminated by improving the form of structure risk in this model, and then the calculating method of the regression coefficients is greatly simplified. Simultaneously, through introducing the composite kernel to the LSSVM, the model can easily adapt to the irregular variation of the chaotic time series. Considering the real-time performance, an online learning algorithm based on Cholesky factorization is designed according to the characteristic of extended kernel function matrix. Experimental results indicate that the unbiased composite kernel LSSVR is effective and suitable for online time series with both the steep variations and the smooth variations, as it can well track the dynamic character of the series with good prediction precisions, better generalization and stability. The algorithm can also save much computation time comparing to those methods using matrix inversion, although there is a little more loss in time than that with the usage of single kernels.