Recursive least mean p-power Extreme Learning Machine

As real industrial processes have measurement samples with noises of different statistical characteristics and obtain the sample one by one usually, on-line sequential learning algorithms which can achieve better learning performance for systems with noises of various statistics are necessary. This paper proposes a new online Extreme Learning Machine (ELM, of Huang et al.) algorithm, namely recursive least mean p-power ELM (RLMP-ELM). In RLMP-ELM, a novel error criterion for cost function, namely the least mean p-power (LMP) error criterion, provides a mechanism to update the output weights sequentially. The LMP error criterion aims to minimize the mean p-power of the error that is the generalization of the mean square error criterion used in the ELM. The proposed on-line learning algorithm is able to provide on-line predictions of variables with noises of different statistics and obtains better performance than ELM and online sequential ELM (OS-ELM) while the non-Gaussian noises impact the processes. Simulations are reported to demonstrate the performance and effectiveness of the proposed methods.