Abstract: It is difficult for extreme learning machine with kernel (KELM) to curb kernel matrix expansion and track the system dynamic changes effectively when it is applied to solve online learning tasks. So the sliding time window method is regarded as the basic modeling strategy, and a new online sparsification learning algorithm for KELM is proposed in this paper. In the process of forward sparsification and backward sparsification, a sparse dictionary with predefined size can be selected by online minimization of its cumulative coherence based on our proposed constructive and pruning strategy. In the process of incremental learning and decremental learning, the model parameters can be directly updated by elementary transformation of matrices and block matrix inversion formula based on the selected dictionary. The performance of the proposed algorithm is compared with several well-known online sequential ELM algorithms. The simulation results show that the proposed algorithm can achieve higher prediction accuracy and better stability, meanwhile, it costs the similar testing time.

Key words: condition prediction, kernel method, extreme learning machine (ELM), cumulative coherence, online sequential learning