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Along with the explosive growing of data, semi-supervised learning attracts increasing attention in the past years due to its powerful capability in labeling unlabeled data and knowledge mining. As an emerging method, the semi-supervised extreme learning machine (SSELM), that builds on ELM, has been developed for data classification and shown superiorities in learning efficiency and accuracy. However, the optimization of SSELM as well as most of the other ELMs is generally based on the mean square error (MSE) criterion, which has been shown less effective in dealing with non-Gaussian noises. In this paper, a robust regularized correntropy criterion based SSELM (RC-SSELM) is developed. The optimization of the output weight matrix of RC-SSELM is derived by the fixed-point iteration based approach. A convergent analysis of the proposed RC-SSELM is presented based on the half-quadratic optimization technique. Experimental results on 4 synthetic datasets and 13 benchmark UCI datasets are provided to show the superiorities of the proposed RC-SSELM over SSELM and other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]