Abstract
A new adaptive sparse least squares support vector regression algorithm, referred to as SLSSVR has been introduced for the adaptive modeling of nonstationary systems. Using a sliding window of recent data set of size N to track t he non-stationary characteristics of the incoming data, our adaptive model is initially formulated based on least squares support vector regression with forgetting factor (without bias term). In order to obtain a sparse model in which some parameters are exactly zeros, a l1 penalty was applied in parameter estimation in the dual problem. Furthermore we exploit the fact that since the associated system/kernel matrix in positive definite, the dual solution of least squares support vector machine without bias term, can be solved iteratively with guaranteed convergence. Furthermore since the models between two consecutive time steps there are (N-1) shared kernels/parameters, the online solution can be obtained efficiently using coordinate descent algorithm in the form of Gauss-Seidel algorithm with minimal number of iterations. This allows a very sparse model per time step to be obtained very efficiently, avoiding expensive matrix inversion. The real stock market dataset and simulated examples have shown that the proposed approaches can lead to superior performances in comparison with the linear recursive least algorithm and a number of online non-linear approaches in terms of modelling performance and model size.