A Quantized Kernel Least-mean-square Algorithm Based on Echo State Network for Online Time-series Prediction

Kernel least mean square (KLMS) algorithm is a popular method for online time-series prediction. It has the advantages of high robustness, low computational complexity, model simplicity, and online learning ability. Unfortunately, as input data grows, its dictionary size increases and the computational complexity rises significantly. In addition, how to improve the adaptability in uncertain environments with noise is also one of the main challenges. In this paper, we propose a Quantized Kernel Least-mean-square Based on Echo State Network (ES-QKLMS) algorithm in response to the above problems. In the new algorithm, the reservoirs of the echo state network (ESN) are integrated with the KLMS algorithm for online prediction. The ESN reservoir can store the associated information of historical data, which improves the algorithm's ability to track temporal characteristics. Then, the vector quantization method is adopted to suppress the size of the KLMS dictionary. Moreover, the adaptive weight adjustment is used to improve the noise immunity in an uncertain environment. At last, The Lorenz time series and the El Nino-Southern Oscillation (ENSO) time series are discussed to demonstrate the efficacy of the ES-QKLMS algorithm.