Extreme Learning Machine (ELM) is a popular machine learning method and has been widely applied to real-world problems due to its fast training speed and good generalization performance. However, in ELM, the randomly assigned input weights and hidden biases usually degrade the generalization performance. Furthermore, ELM is considered as an empirical risk minimization model and easily leads to overfitting when dataset exists some outliers. In this paper, we proposed a novel algorithm named Multiobjective Optimization-based Sparse Extreme Learning Machine (MO-SELM), where parameter optimization and structure learning are integrated into the learning process to simultaneously enhance the generalization performance and alleviate the overfitting problem. In MO-SELM, the training error and the connecting sparsity are taken as two conflicting objectives of the multiobjective model, which aims to find sparse connecting structures with optimal weights and biases. Then, a hybrid encoding-based MOEA/D is used to optimize the multiobjective model. In addition, ensemble learning is embedded into this algorithm to make decisions after multiobjective optimization. Experimental results of several classification and regression applications demonstrate the effectiveness of the proposed MO-SELM. (C) 2018 Elsevier B.V. All rights reserved.
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