Online parameters updating method for least squares support vector machine using Unscented Kalman filter

Abstract

It is well known that the performance of Least Squares Support Vector Machine (LSSVM) is guaranteed by k-fold cross-validation (k-CS) or other optimized approaches to choose an appropriate setting of a number of parameters including such as the regularization parameter (7) and the kernel parameter (σ) and so on. However, it is mentioned in a large number of research on k-CS that it need more computational time and large computational burden in the process of optimizing parameters for LSSVM. Moreover, the obtained parameters by CS method are fixed and it lead easily to a poor generalization capabilities in various application. In order to avoid k-CS and to implement parameters update online, this paper proposes a novel method which applied Unscented Kalman Filter (UKF) to dynamically implement parameter updating problem for LSSVM. To estimate LSSVM's parameters online, the state and measurement equations of UKF are first constructed by considering LSSVM's parameter choice as state variable and treating LSSVM model as the measurement equation, respectively. Then, the UKF approach is used to update the LSSVM parameters timely according to the last obtained instance. Applying the proposed method, LSSVM parameters are not any more fixed as tuned parameters on the training dataset, but are adjusted dynamically as new measurements arrived. Finally, the viability and superiority of the proposed method are verified by simulation.