Multiple adaptive kernel size KLMS for Beijing PM2.5 prediction

The kernel least mean square (KLMS) algorithm is an efficient non-linear adaptive filter that operates in the reproducing kernel Hilbert space (RKHS). In realistic applications of system identification or time series prediction, there are usually multiple inputs that demand multiple kernels or kernel parameters. This paper proposes to use a tensor product kernel for KLMS that accommodates multiple inputs. Furthermore, instead of arbitrarily setting kernel parameters, appropriate kernel sizes can be chosen by a gradient descent based adaptive algorithm that minimizes the square of instant error, which helps KLMS to better capture the underlying system mechanism. Effectiveness of the proposed algorithm is shown by experiments conducted for both simulated dataset and an important real-world problem - Beijing PM2.5 prediction.