An improved kernel-based incremental extreme learning machine with fixed budget for nonstationary time series prediction

In order to curb the model expansion of the kernel learning methods and adapt the nonlinear dynamics in the process of the nonstationary time series online prediction, a new online sequential learning algorithm with sparse update and adaptive regularization scheme is proposed based on kernel-based incremental extreme learning machine (KB-IELM). For online sparsification, a new method is presented to select sparse dictionary based on the instantaneous information measure. This method utilizes a pruning strategy, which can prune the least “significant” centers, and preserves the important ones by online minimizing the redundancy of dictionary. For adaptive regularization scheme, a new objective function is constructed based on basic ELM model. New model has different structural risks in different nonlinear regions. At each training step, new added sample could be assigned optimal regularization factor by optimization procedure. Performance comparisons of the proposed method with other existing online sequential learning methods are presented using artificial and real-word nonstationary time series data. The results indicate that the proposed method can achieve higher prediction accuracy, better generalization performance and stability.