A joint optimization framework to semi-supervised RVFL and ELM networks for efficient data classification

Due to the inefficiency of gradient-based iterative ways in network training, randomization-based neural networks usually offer non-iterative closed form solutions. The random vector functional link (RVFL) and extreme learning machine (ELM) are two popular randomized networks which provide us unified frameworks for both regression and multi-class classification. Currently, existing studies on RVFL and ELM focused mainly on supervised tasks even though we usually have only a small number of labeled samples but a large number of unlabeled samples. Therefore, it is necessary to make both models appropriately utilize both labeled and unlabeled samples; that is, we should develop their semi-supervised extensions. In this paper, we propose a joint optimization framework to semi-supervised RVFL and ELM networks. In the formulated JOSRVFL (jointly optimized semi-supervised RVFL) and JOSELM, the output weight matrix and the label indicator matrix of the unlabeled samples can be jointly optimized in an iterative manner. We provide a novel approach to optimize the JOSRVFL and JOSELM objective functions. Extensive experiments on benchmark data sets and Electroencephalography-based emotion recognition tasks showed the excellent performance of the proposed JOSRVFL and JOSELM models. Moreover, because the direct input-output connections help to regularize the randomization, JOSRVFL could obtain superior performance to JOSELM in most cases. (C) 2020 Elsevier B.V. All rights reserved.