Sparse Recursive Least Mean p-Power Extreme Learning Machine for Regression

Real industrial processes usually are equipped with onboard control or diagnostic systems and limit to store a complicated model. Also, measurement samples from real processes are contaminated with noises of different statistical characteristics and are produced by one-by-one way. In this case, learning algorithms with better learning performance and compact model for systems with noises of various statistics are necessary. This paper proposes a new online extreme learning machine (ELM) algorithm, namely, sparse recursive least mean p-power ELM (SRLMP-ELM). In SRLMP-ELM, a novel cost function, i.e., the sparse least mean p-power (SLMP) error criterion, provides a mechanism to update the output weights sequentially and automatically tune some parameters of the output weights to zeros. The SLMP error criterion aims to minimize the combination of the mean p-power of the errors and a sparsity penalty constraint of the output weights. For real industrial system requirements, the proposed on-line learning algorithm is able to provide more higher accuracy, compact model, and better generalization ability than ELM and online sequential ELM, whereas the non-Gaussian noises impact the processes, especially impulsive noises. Simulations are reported to demonstrate the performance and effectiveness of the proposed methods.