Sparse KELM Online Prediction Model Based on Forgetting Factor

In the process of online prediction of nonstationary time series by kernel extreme learning machine (KELM), two problems appear that the order of kernel matrix is increasing and the system dynamic characteristics are difficult to be determined. A sparse KELM state prediction model based on forgetting factor (FF) is proposed. Firstly, by introducing the forgetting factor, a new objective function is constructed to make the elements in the sparse dictionary have different weights according to the time distance, so as to ensure the effective tracking of the dynamic changes of the model. By studying the relationship between KELM and kernel recursive least-squares (KRLS), KRLS is extended to the online sparse KELM framework. To control the growth of network structure, and realize the recursion and update of dictionary parameters, the samples are sparse by using approximate linear dependence (ALD) criterion. The experimental results show that compared with KB-KELM, FOKELM, NOS-KELM and KRLSELM, FF-KRLSELM can reduce the average root mean square error by 48% and 36%, and the average relative error by 37% and 36%, and has good dynamic tracking ability and adaptability.