| Summary: | Semi-supervised extreme learning machine (SS-ELM) has been applied to many classification and regression assignments with high performance, in which both the labeled and unlabeled data are exploited to enhance accuracy and computation efficiency. The Laplacian manifold regularization method has been incorporated to explore the geometry of the underlying manifold structure. However, the Laplacian manifold regularization lacks the extrapolating ability and biases the solution to a real constant function. In this paper, we propose a novel algorithm, the Laplacian-Hessian regularization SS-ELM (LHRSS-ELM), to enhance the performance of conventional SS-ELM. The main advantages of LHRSS-ELM are as follows: 1) LHRSS-ELM exhibits the learning capability and computational efficiency of traditional SS-ELMs; 2) LHRSS-ELM algorithm combines both Laplacian and Hessian term to enhance the extrapolating power, accuracy, and robustness and also show significant performance in multiclass classification tasks; and 3) for the purpose of pursuing the best pair of hyperparameters to establish a comparable model, we dynamically update them from sequences. The proposed algorithm is evaluated on publicly available data sets and further applied for the state classification of superheating degree in the aluminum electrolysis process. The experimental results demonstrate that the proposed mechanism is superior to the existing state-of-the-art semi-supervised learning algorithms in the matter of accuracy and robustness.
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